You first need to stabilize the stretch. Since the lycra does not like heat, I would consider using a spray basting to afix them to either a interfacing or muslin base then baste the perimeter . When cutting the fabric ..cut larger , then once afixed trim , then baste using a slight zig zag stitch. Do use a ball point needle for this work.
If you have not worked with alot of knits .. this may very well not be a project you want to tackle.
Just my opinion ... this is has the potential to be a very large pain in the ..... project.