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.
