I have a strong doubt that a paddle will stay in place with Lycra. A 1911 weighs something in the neighborhood of 30-45 ounces loaded up. Lycra is intended to be flexible and comfortable, NOT to hold weight.
I suggest that you get a standalone gun belt, and use whatever belt holster you prefer, but be sure it can retain it in case of a crash. If you are particularly skinny, this will quite possibly lead to the belt riding up your waist, potentially being uncomfortable and making draws difficult, especially if the belt is sitting on the fabric as opposed to bare skin. A cure for this is to carry cross draw, and as Sonora Rebel calls it "slap leather" with your weak side as you draw. How rigid the belt is, how snug it is, and how you are shaped will all be important factors to consider in making a rig work for you. It has to be just right, because cycling, especially fast, is obviously an involved and demanding task with a lot of different motions that a rig has to work with.
Testing this should be easy, just take belt holster, or even a paddle hooked to a belt, belt it up around your waist, and go for a ride. I have been doing this for several years, and I am happy with it.