That's a hard question to answer, as with lycra there is never a set percentage on thread ratio.
For instance. a 4 way stretch lycra with:
70% lycra, 30% Polyester
-will probably retain it's shape very well. That kind of lycra is mostly what you would see in Under-armor or Zyflex sports wear. I believe most spidey suit makers are using this kind of lycra so I'd say go for it.
However, If it is:
40% Lycra, 60% Cotton.
A cotton based lycra is not going retain it's shape as easily, and you'll have to wash it periodically to get the "over-stretch" out.
VERY few Spiderman suits use this kind of lycra nowadays though... but I know it was the prime choice for dye-sub back when we started making suits because the transfer heat can be high without melting the plastic in poly thread.
A sort of odd-ball in the Lycra group however, is Milliskin.
This stuff, I notice, is particularly thin (low thread count) for a lycra... and after being worn does have a tendency to over-stretch simply because there aren't as many elastic fibers to pull it back into place.
This was another big spider-suit material... so if you have that, I'd be more worried about it.
All of these you can determine by feeling the material.
Does it feel like an under-armor shirt?
Does it feel soft and somewhat fuzzy like cotton?
Is it somewhat "sheer" or is it very thick?
More importantly, pinch the fabric and pull it in all four directs. How readily does it want to return to it's natural state?