When I was heavily into road cycling (tight shorts, loud jersey, dorky helmet, drop handle bars etc.), I carried my LCP with a round chambered, in a pocket holster, in my right rear jersey pocket, and the pocket holster was in a zip lock bag. Was it immediately available in a hurry? No, but at least I wasn't defenseless.
I rode this way for thousands of miles. The mathematical average of all my rides was 31 miles. In 31 miles, a road cyclist generates lots of sweat, summer or winter, hence the zip lock bag.
With my LCP carried in the manner described, I had no issues at all, and in 62,000 total miles on the road, fortunately, never needed to use the LCP.