If i would be a DM, i would allow only a singular patron for Githyanki warlock.
Reason obviously is a lore. GIthyanki loyal to singular entity - their lich queen. Well, unless you are githvyrik exile/traitor (which would be another unique background for giths).
I understand that many other ppl would be as much lore-suckers as i am. Still, adding Vlaakith as an unique warlock patron, available only to githyanki - would really support game immersion.
And if you would go for such immersion, i would also forbid Githaynki picking cleric class (again, unless player would pick githvyrik background). Vlaakith haven't achieved true godhood yet, and again, true githyanki wouldn't worship anyone else.