The word stay here means stop or pause. From Merriam-Webster:
intransitive verb
1: to stop going forward : pause
2: to stop doing something : cease
Or from the Macmillan dictionary:
4 [transitive] formal to stop something such as a court case from continuing
The defence has filed a petition to stay proceedings.
The sense is:
If the lady stops her weaving in order to look down to Camelot, a curse will take effect.
The lines you've quoted are from the 1842 version of the poem, which uses stay intransitively and obscures the sense a bit. The corresponding lines in the 18321833 version use the verb transitively, and make the sense clearer:
No time hath she to sport and play:
A charmed web she weaves alway.
A curse is on her, if she stay
Her weaving, either night or day,
To look down to Camelot.
(Emphasis added)
That of course is exactly what happens. The lady sees Lancelot in the mirror, stops weaving, and rushes to the window to catch a further glimpse of him as he rides down to Camelot. This sets the curse in motion.