By the rules, becoming a lich is a willful and voluntary action on the part of the would-be lich. You can’t do it for someone, and you can’t have it done to you. You cannot even be forced or tricked or mind-controlled into it:
The process of becoming a lich is unspeakably evil and can be undertaken only by a willing character.
Furthermore, the rules also state that
"Lich" is an acquired template that can be added to any humanoid creature
Which means that raising him as some other form of undead isn’t useful.
Thus, you are left with resurrection or similar; resurrection is a 7th-level spell, so the caster has a minimum of Caster Level 13th, which means anyone who died in the last 130 years, minimum, is a valid target. That includes your guy. He could then become a lich through the usual process.
A 10th-level cleric could cast resurrection from a staff, or from a scroll with an easy Caster Level check (DC 14 and he’s got a minimum of +10).
If the body is unavailable, you need true resurrection, a 9th-level spell (minimum Caster Level 17th), and that’s a somewhat more difficult DC 18 Caster Level check (still a 65% chance to succeed)
Narratively, though, that might fall a bit flat. I know of no direct raise-as-a-lich spell. However, depending on the details of the afterlife in your setting, there may be another option. A character must be humanoid to become a lich, and must create his own phylactery. Nothing says he has to be humanoid when he creates his phylactery. Perhaps his spirit creates the phylactery, before being raised, and then there’s a combination ritual: a cleric casts resurrection on him as he performs the ritual to become a lich. This seems more interesting and dramatic. He’ll still briefly return to life, but only briefly. Easily explained as trying to limit his vulnerability (I imagine a scroll of resurrection is a bit tricky to come by).
If you're only using content from the SRD and your original work, then you can release it under OGL.
A conversion of someone else's non-OGL rules from a previous version would not be allowed under the license.
The Book of Vile Darkness is "product identity" per page one of the SRD/OGL for D&D Fifth edition. Items marked as Product Identity ... are not Open Content.
Best Answer
Outside materials for particular campaigns, there is only one official way for a PC to become a lich. The Book of Vile Darkness is detailed in the 5th edition Dungeon Master's Guide (p222). It doesn't describe the ritual to any great extent, leaving it largely in the GM's domain to determine what steps a character aspiring for lichhood ought to take. Some guidance can be garnered from the Monster Manual, though, on creating plotlines for your characters to become liches without the book.
Under the normal monster lore, a wizard can become a lich only through a pact with various evil planar entities, as described in the 5th edition Monster Manual:
The process to become a lich involves the sacrifice of the soul of a sentient creature:
The phylactery requires regular soul sacrifices to prevent the lich from devolving into a demilich. The heavy measures needed to sustain lichhood are so extreme and repulsive that it takes a truly evil character to embark upon this road...
...unless...
Blast from the past: Archliches
Assuming you're ok with adapting material for earlier editions, at least in the third and fourth editions there is a good-aligned variant of the lich: the Archlich. No official 5th edition material exists for Archliches as far as I know. The 4th edition source materials for Archliches describe them as choosing lichhood as a means to a noble end, not as an end in itself, and diligently learning the rituals involved as opposed to taking the easy path of acquiring the secrets of lichhood from Orcus or other fiendly creatures. Archliches retain their personalities and memories, and are not mentioned to need soul sacrifices to avoid becoming demiliches.
While Archliches offer a way for non-villainous characters to reach lichhood, lore-wise the ritual to reach this state has to be hard enough to discourage even most talented spellcasters from choosing this route instead of Orcus's support.
Campaign-specific methods
According to the user blade, a method for becoming a lich is detailed in the Curse of Strahd campaign materials. I do not know this method personally, because I am going to participate in a CoS campaign myself and don't want to spoil anything about the module to myself. If you have a copy of the CoS materials, you can look it up yourself.