I now had doubts because of the designation. Since I have not had as much experience with it, I was skeptical whether one can simply use any 58mm cover. On the page with Olympus lens delivery was the lens cap LC-58E. This I found however nowhere. The LC-58E was 4/3 lens on my Mirco and was very shallow. The offered here LC-58C, however, was very different and was thicker.
My concerns were completely unfounded, the lid is very valuable and is keeping super on lens, I can only recommend.