I actually think Lae'zel would be an Eldritch Knight just because of the culture she comes from. The term Gish is literally a Githyanki word that got adopted by the community to refer to martial spellcasters. She aspires to earn a Silver Sword and ride a red dragon one day. To become a knight she needs to have both a high level of martial skill and a high level of psionic prowess to prove that she is worthy of the station.
I suppose technically that'd make her a Psi Warrior, but as that isn't in the game Eldritch Knight is the best representation for the sort of Gish battlemage that Githyanki knights are meant to be.
Ditto to this.
I’d also say that Astarion to me makes the most sense as an arcane trickster, as the cantrip Friends alone would make his job far easier, let alone disguise self, minor illusion and the like.