"To become a psychic lich, one must create and infuse a memoir, which serves a similar function to an ordinary lich’s phylactery... Each psychic lich must create its own memoir by using the Craft Wondrous Item feat. The character must be able to cast psychic spells at a caster level of 11th or higher. The memoir costs 120,000 gp to create and has a caster level equal to that of its creator at the time of creation."
So do you still have to do the Eternal Apotheosis or does the crafting of the memoir create the Psychic Lich?
Of course for a regular lich Eternal Apotheosis isn't required. That is just one path of many. So since Eternal Apotheosis isn't required for a regular lich, it almost certainly isn't required for a Psychic Lich.
So the real question is, is creating a memoir enough for a psychic lich and if not, what else is required?
Psychic lich doesn't specifically say. It does say though that along with creating it, the lich also has to infuse the memoir, a process that isn't defined or explained. It also says that it is similar to a liches phylactery, and of course just making the phylactery isn't enough. A regular lich has to 'learn the secrets of transferring his soul' and that sounds pretty similar to 'infusing a memoir' to me, so I suspect a similar process is required for a psychic lich.
Exactly what that would be would probably vary from one individual to another, just like it does with regular liches. Personally, I wouldn't let eternal apotheososis itself ever work, but their being a special ritual for a psychic transformation isn't impossible. The best course though is to have it be tailored for each individual, but the level of difficulty to accomplish should at least be as hard as the eternal apotheosis ritual.