Yes, I use my LC on my ceramic top stove all the time -- like at least twice a week -- and have been doing so for 6 years. It works beautifully. Just as well as they worked on my previous gas cooktop.
I also use my cast iron skillets on the ceramic stove and
one of them does not have a flat bottom -- it has that little ring. Guess what? It works just fine.
My guess is that the issue with using them is more about how heavy they are. You need to be careful not to drag them on the cooking surface ever. And dropping a LC french oven would no doubt break the cooktop. So it goes without saying that you need to be extra careful in handling them.
Performance-wise, I have had no problems whatsoever.