If someone takes the phylactery of a Lich, and carries it off, and then someone else "kills" the Lich, it reappears near the phylactery. But if the Lich is basically a wizard, then wouldn't it have to relearn all the spells? In that case, if the spell books weren't around (the phylactery wasn't in the lair after all), then what powers does the rejuvenated Lich have? Would it then have to go back to the lair for the books? When a Lich travels, it must at least carry a copy of the books, right? Those books would be left behind with the newly destroyed Lich, I would imagine. Just trying to think through how all this might play out.
No, the rejuvenated Lich should still remember all its prepared spells
There is no rule that states that a character forgets their prepared spells if they are killed, and no rule that states they cannot remember them upon being resurrected, either. A wizard's list of prepared spells only changes if they decide to prepare a new list after a long rest or some other effect specifically alters the list - dying, and coming back to life, has no effect on the list. Likewise, when the Lich rejuvenates into a new body, it should remember all the spells it had prepared before it was destroyed, since there's no rule that states it forgets them. It should even retain any unused spell slots it had when it was destroyed.
Previous editions did have some rules to this effect, specifically that in 3/3.5e a spellcaster revived by raise dead has a chance of forgetting some of their prepared spells:
A character who died with spells prepared has a 50% chance of losing any given spell upon being raised [...]
But language like this is notably absent from all the resurrection-type effects in 5e.