Since githyanki are all about psychic damage, I can see her taking levels as GOOlock for those sweet psychic spells and abilities. Make her a bladelock and you can give her maybe 5 levels in lock and the rest in fighter.
If aberrant mind sorcerer were in the game, I totally would give her that class and two levels of fighter.
Otherwise monk would make sense for her, it is a martial class, but all about controlling yourself,which I think, is totally Lae'zels thing, even though,she can be pretty impulsive sometimes ( which I would say is due to her youth).
I once tried 11 fighter/ 1 GOO warlock with her, tried to capitalize on low critical threshold, used Unseen Menace, champion subclass, polearm master for a guaranteed additional attack (crit fishing, hehe). Also envisioned it in a sort of "falling under your sworn enemy's influence" way. Tadpolearm master, you know? For spell utilization though, vanilla Laezel experiences some charisma issues, 8 for starters is horrible...
Since she has half decent WIS, I wanted to lean into some WIS spellcasters, monk seems fine in this regard, but my recent PT was as a pure monk and I got tired a bit. The big idea is to justify putting at least 1/3 levels into druid or ranger (or cleric, but I already have one) so that it feels organic to the story. No Gale barbarian level of vibes, I mean.