I have cut up and joined two pieces before, but this was on a topper.
As Paul says, you need to use a head to work out the shape of what you're cutting and joining.
To maintain the curve and keep the whole thing fitting properly, the shape & seams to be joined won't be what you would necessarily think they'd be.
If you cut out the balding bit, you would use that as your template for the new piece, but cut the new piece a bit bigger all round.
Then, as again I think Paul said, you need to make a boarder of lace on the new piece that is hairless.
I have shaved the lace before and its worked, but you need to be careful.
I use see-thru nylon thread to sew the seams and make very tiny stitches from the underside that are looped through the holes of the lace.
You just have to be careful afterwards not to brush or comb the piece too hard.
Doing this should give you enough time to order a new piece, but you may have to restitch it the meantime.
Best of luck.