Every so often, pick a theme and announce a fashion contest to happen the following week. It can be tricky to find a moment when people are listening enough to announce it, so it might take a few tries.
The limits in what we can dress up as in LOTRO should inform what kinds of themes you choose, but don't fall into the habit of choosing themes based on what our wardrobes do well. For instance, "fancy dresses" is an easy one, because LOTRO has a lot of those, but that also means it's not that challenging a contest, and besides, you can only do that one so many times. The best themes don't really correspond to obvious choices but give people some latitude in being creative. For instance, a theme of "outfits in blue" gives a lot of latitude for people to find off-beat and creative outfits that are all different from one another.
People can be surprisingly shy about dressing up and then showing off their clothes. Best way to break the ice is to find someone you know is a real ham with no shyness and get them to go first. Egg them on to twirl and show off, to tell a story about the outfit, to put on a show. While you might think this would make other people even more shy (in the "I can't live up to that!" sense), it actually seems to draw people out instead.