Perhaps I can just cite "The Singing Springing Lark" and say she can't fly that far without resting. Or perhaps that she's not any faster than walking, thus burdened, and so they should walk. (Her father could fly farther on his. A different sort of gryphon?)
She can't lose the ability to change forms because she's going to need it at the climax.
And all this because I decided a lion wasn't plausible enough.
Eh, don't think I'll change it back. (Or that they have to fight his gryphon -- that will keep them from flying out, too. So they won't arrive in time for certain other events. Such is the effect of parallel plotlines.)