The Adventure Cycling store sells two pair of non lycra form fitting shorts. Baggy shorts. Canari and J&G brands.
It's not Lycra I have an issue with. It's the "form-fitting" aspect.
Then you do have an issue with lycra. Lycra is a stretchy material designed to form fit and stretch around whatever it contacts. It has elastic in it. You want the baggy cargo shorts everyone has recommended. They are NOT made out of lycra. They are made out of nylon and polyester. Personally I can't imagine this short is as comfortable for riding as the lycra shorts. The lycra short keeps the chamois in place by stretching it around the part of the body its supposed to be at. Whereas the cago baggy shorts are loose around the chamois. So the chamois can slide around and move while you are riding. Not ideal.