She is carrying her thought out toward that part of the arena, or beyond, where she wants to be. So, when you lift your left rein (oh, are you direct reining or neck reining?) she may move her head over toward the left, but her thought, and her shoulders and body go right . Correct?
She is not longer following the rein. For that, I would contincue to lift the left rein, saying "here, it's here!", maybe bump it a bit to see if I can get her attention, and if she drifts out, I'd disengage her entirely, and then ask her to step out left again , following the rein. If during the disengagement, she ends up not facing the direction you want her to go, it doesn't matter. Your objective is to get her to follow the left rein.
So, you lift the left rein againg, ask her to step left and head off, and then when you steer her toward the way she has trouble, keep in mind that if she stops following your directing rein, and is bowing out through her shoulders, you disenage, and ask again.
Of course, you can also support her following your leading rein by keeping your outside leg on her a bit to discourage her from drifting out, but if she ignores that, leans on your directing rein and barges through, disengage, and try again.