[RPG] How to the necromancer become a Lich

Yes, this spell will control a lich.

Control Undead states:

This spell enables you to control undead creatures for a short period of time. You command them by voice and they understand you, no matter what language you speak. Even if vocal communication is impossible, the controlled undead do not attack you. At the end of the spell, the subjects revert to their normal behavior.

Intelligent undead creatures remember that you controlled them, and they may seek revenge after the spell's effects end.

So "Intelligent undead" can be controlled; however the Lich has several lines of defence against this spell.

• Max 2 HD/Level spell limit. Although admittedly not much of a barrier.
• Will save. The lich is going to have a VERY large bonus for this.
• Spell resistance. And probably this as well.
• Spell Immunity, Greater. Any self-respecting lich will know this spell and have "control undead" as one of the spells it's immune to. Wouldn't you?

Note also, any lich is going to know this spell and have ways around it. The only thing the lich is restricted from (initially) is attacking the caster this isn't going to stop them (until commanded) from...

• Teleporting away.
• Casting silence around themselves so they can't hear you
• Attacking any of your allies.
• Perverting the words of anything you say. "Where is your phylactery?" (The lich answers in Abysmal, which the player doesn't speak.) "Tell me in Common where your phylactery is?" (The lich says "It is under the sacred cloth of my father.") and so on... all buying it time to get away.
• And so on.

It's not a hands-down game winner against a Lich,

I wanted to all an alternative from all the other types of posts I see (which more or less assume this is possible). That being said this is more my interpretation of how the rules are supposed to be viewed.

The rules for how you gain new spells as a wizard are fairly clear - you gain them as you level, based on your spell book. Now that being said, it is my assumption that a Wizard is already using his downtime to learn new spells, update his notes, and in general improve his spells. My example to support this is that a fighter doesn't just go to town, sit down and drink/sleep all night (well fair point, some probably do). But most are probably training, practicing their weapon skills, or improving themselves.

I would say the rules for Wizards also support this...

The spells the you add to your spell book as you gain levels reflect the arcane research you conduct on your own

Since if you are not doing this research in your down time, when are you doing it?

Aside: Now, it would be a separate issue if say the Wizard found a spell book, or notes about some spells he did not already know. But this strikes me as more of the role-playing side, and I don't intend to cover that in my answer.

If you decide to allow it, I would highly recommend making it massively less useful for your Wizard. A good method would be to use the spell copying table mentioned in other answers and use that as the time required (I expect this would dissuade him from trying anything other then the lowest level spells). It seems the rules outlined for this (both time and money) are fairly penalizing - I might also add a failure chance for a bit of home-brew flavor as well (e.g. the Wizard was attempting to write a spell he did not already know and did not gain through practical use).