I'd easily believe Lae'zal bears her "regal name" with a full right, in a hierarchical, orderly nation;
But it's not simply birthright. For a wild guess, she is from a "privileged" egg batch, but for now, reading Mordenkainen Tome of Foes, where the latest githyanki lore is told, I'm glad to see Larian just follows the lore given by someone else without trying to twist it for any reason.
Lae'zel behaves as normal githyanki would, even her arrogance toward the knight's orders seem normal; he can order his subordinates, but not her until she is in his squadron (which she wouldn't be).
