I like the concept a lot! I definitely don't think it's overpowered -- it might be underpowered, but not excessively so, in my opinion.

I think the main issue with this class (which I mention several times in the below points) is that its most powerful feature is Serenity's Shadow which it gets at 1st level. This has 2 issues: it encourages other classes to take a 1 level dip in this class, rather than sticking with it, and it makes later levels kind of boring, since you don't gain as much from later levels. I'd try to spread the power of Serenity's Shadow over multiple levels and I provide a few suggestions for that below:

• Serenity's Shadow:

  1. You should specify that the radius is centered on yourself.
  2. Can any creature be made Vulnerable, even if they'd otherwise be immune?
  3. How long does the advantage on Stealth last? Since DMs often use one check to cover an extended period of stealth, is it ok if the advantage lasts a long time, or it it meant to only apply for the short period before the shadow retracts?
  4. I worry that the Vulnerability feature is a bit weak, since it only applies to a single attack and then reduces your AC for the entire day. @BlakeSteel points out that increasing its duration could be overpowered if other characters coordinate their actions to exploit it, but I see little issue with allowing it to apply to all of your attacks this turn (if you have Extra Attack, Thirsting Blade, Haste, or Two-Weapon Fighting or another form of Bonus Action attack).
  5. The main concern with this would be that it makes a 1-level dip extremely powerful. Moving that feature to a higher level would solve that problem, and give a nice boost to higher levels for a class that gets most of its best features at 1. So, at 1st level, it would only apply to a single attack, while at Level 10, it could apply to all attacks on your turn.
  6. If you're worried that the change in 4) is too powerful, you could make it kick in only at a higher level, and/or make it shift Vulnerability by one category: so Normal -> Vulnerable, Resistant -> Normal, or Immune -> Resistant
  7. To make this feature a bit clearer, I'd tie the number of uses to casting the shadow, then list the benefits while the shadow is out, and then list the actions that can be taken which use up the shadow. This way, you don't have the phrase "Once the shadow is used in this way, it recedes until you have taken a long rest", which becomes invalidated once you get multiple uses at 10th level.

• Serenity's Shadow - AC Bonus:

  1. Since the AC bonus is worded as a flat bonus to AC, it would stack with the Monk's WIS bonus to AC, the Barbarian's CON bonus to AC, or the AC bonus from Mage Armor. Is this intended? If not, you should mimic the wording of those features and describe it as an alternate way to calculate base AC.
  2. I don't think letting the AC bonus stack is overpowered, but my main worry is that, since the feature is gained at Level 1, it would encourage 1 level dips, just to get the AC bonus. It's really flavorful, and I like getting it at 1st level, but you should find some way to make it scale with level to discourage 1 level dips
  3. Here's one suggestion for scaling: Let the shadow only be active for a limited number of turns per use (perhaps 1 + Warlock level). So, a 1 level dip would give you a free AC bonus for only 1 or 2 turns per day; good, but not overpowered. At level 5, it's probably safe to make it last indefinitely, since that's a significant investment.

• Severance:

  • Is it meant to have unlimited uses (assuming you have hit dice remaining)?
  • The wording on this is unclear. I'd reword it to mimic the Durable feat:

    "you can use an action to roll one Hit Die to regain hit points, the amount of hit points regained is equal to the die roll plus your Charisma modifier"

• Planar Doorman:

  1. The section that states: "You can also immediately identify the plane ..." I assume this refers to the location they're going to plane shift to, right? That's unclear from the wording.
  2. The first clause should mimic the invocations that add spells: "You can cast plane shift once using a warlock spell slot. You can’t do so again until you finish a long rest. If you are traveling to Sigil, this does not use a spell slot or material components".
  3. Does the reaction to counter plane shift also use up the free planeshift? Does it prevent you from tracking people who try to plane shift?
  4. I think it would be cool if, instead of just countering the casting of plane shift, you also had the option to use plane shift to follow that person.

• I thought you were a deader for sure!:

  • Does this ability only apply to yourself?
  • This ability is pretty underpowered, since most DMs don't give their PCs crippling injuries. I'd expand the healing potential by giving you the change to cast Regenerate as a Warlock spell once per day, perhaps with the side effect of it being excruciatingly painful.
• Restrictions and Benefits:
  • As Miniman points out, the ability to navigate the City of Doors listed under "Restrictions and Benefits" looks like fluff or a roleplaying hook, but could actually be extremely mechanically powerful, especially if the campaign takes place in Sigil.
  • No other patrons have mechanical benefits in their description - if you want this to be a specific power that Lady of Pain Warlocks have, you should make it a class feature, perhaps part of Planar Doorman
  • A better option, in my opinion, would be to remove any explicit powers of navigation and, instead, state that the Lady of Pain can, at her discretion or in exchange for a deal/favor, grant this power to assist players in carrying out her will. This puts control of the feature in the DM's hands and reduces the odds that you'll disrupt the campaign by intuitively navigating to the BBEG's secret lair.

This answer is going to come off as extremely negative. Unfortunately that is my best analysis of the class. So before I get into I want to say; I love the theme of what you were going for. A patron that could be a level 20 character from a previous campaign is great. I also don't want to discourage you from homebrewing stuff in general, this class has a lot of issues though and I felt it was necessary to point them out.

This is unbalanced and breaks the style of warlock patrons

This patron makes such a departure from the typical structure of a warlock patron that it is somewhat difficult to assess in balance terms. My gut says it is very over-powered and I will try to go through each feature to explain why. Note; this analysis is focused on comparing it to other patrons not the entire warlock class.

Expanded Spell List

A standard feature of warlock patrons that you have re-interpreted, both in good and bad ways. Overall your version is overpowered and needs to be fixed.

Spell List As Spells Known

The PHB patrons get access to 2 spells of each level from 1st to 5th. They are simply added to the spell list and do not add to spells known. The celestial and hexblade patrons from XGtE only get access to 1 spell of each level but they still do not count as known spells.

Expanding the spells known of the warlock is completely against the design of all other patrons. This part of the feature is completely broken and needs to be removed.

@illustro points out that as worded this does not add additional spells known but instead forces the warlock to learn those spells. If this is the case then this feature is actually extremely weak, far worse than any of the other patron spell list options.

Choice of spell list

The choice of three different lists based on the spellcasting class of the patron is a cool thematic choice. However all three lists contain spells that are already available to the base warlock. The warlock list is worse than useless, while major image from the wizard list and banishment from the sorcerer list are already available to warlocks.

I would like to see this feature remain but it needs work on the spells chosen. I would drop the warlock list and a add bard, and/or druid list instead.

Lesser Mystic Arcanum

Nope. This feature is entirely broken. At 9th level your warlock has an additional 5 spell slots per day above and beyond their typical 3 per short rest. Not all warlock spells benefit from up-casting and having them in lower level slots does not sufficiently reduce their power. Giving this many additional spells is way, way stronger than anything any of the other patrons give at this level or at any level.

There is no point even comparing this to the other patrons in detail. In summary it is very overpowered and needs to be removed entirely.

Strategic Spell

This one isn't too bad. Rogues and monks already have access to this feature. However it does go against the normal style of the warlock. Apart from the celestial patron every other patron grants a once per short rest ability not an always on feature. By not being limited to pact slots this feature works on cantrips and is therefore infinite.

To answer your follow up questions, removing Dash makes no real difference, Disengage and Dash are about equal. And no; you absolutely should not include Dodge. Dodge is way stronger than either of the others, there is a reason rogue's cunning action does not include it.

This feature is likely a little overpowered due to unlimited uses, but only when compared to the other warlock patrons. Overall this feature is not game-breaking given you should be at range anyway.

Eldritch Weave

At first this one seems ok, but it is likely overpowered. Gaining temporary hitpoints is very similar to the Celestial Resistance feature of that patron, though that one allows you to also protect other creatures.

The issue with this feature is the additional feature: "your concentration cannot be broken until you lose all of these temporary hit points". This is extremely strong. Spellcasters typically take entire feats (War Caster, Resilient (Con)) just to buff their concentration checks. Your feature is negating them entire for a minute.

Yes, this benefit ends early if you get hit enough. But, at a minimum of 20HP and increasing every level this will take a few rounds. Assuming you are concentrating on some disabling spell like hold person or similar it might be impossible for the enemy to deal enough damage to break this before your party takes out your target.

This feature is overpowered and should be changed.

Greater Mystic Arcanum

If the early version of this feature wasn't so utterly unbalanced this would almost be fine. However; it isn't, and neither is this. At will hex at 14th level, then suggestion at 18th level is very powerful.

In fact this feature is exactly eqivilent to the 18th level Spell Mastery feature of the wizard, barring some flexibility. No other patron gets a feature anything like this. Several only get a single once per long rest ability.

At will casting of leveled spells is normally restricted to Eldritch Invocations. Allowing it in addition to those completely breaks the style and design of the Warlock. This is utterly unbalanced and needs to be removed.

Conclusion

Scrap the whole thing. The features are almost all overpowered and don't suit the style of the Warlock at all. Any one of the features (bar Strategic Spell) would be enough to make this class overpowered. Added together this is completely busted.

You are adding flexibility by increasing spells known with your 1st level features, and you are increasing overall power level by giving out way more spell slots. This Warlock is so much better than the others there is almost no reason to look at them unless you want to be a melee fighter.

Back to the drawing board for this one.