The Lycan Mouse is now a regular sight on Mousehunt. Back in the days of it's introduction (see below) it was the badge of honor that mousehunters wore everywhere. Now.. meh..
For newer hunters, your first is probably the hardest. You'd need to catch the one in the Mousoleum that drops the Furoma Map Piece. Either the Ambrosial or the Sinister Portal's the best shadow trap that you can afford at this time. Radioactive Blue, or better yet Moon Cheese if you got some.
I prefer using the strongest+luckiest base I have available, since stales like radioactive sludge or stale cheese are not too much of a worry anymore. If you're here now, your best is probably only the Explosive Base (Yes, it still works). If you were around for one of Ronza's visits or the Christmas Festive Comet, you'd probably have the Magma or Gingerbread (the power multipler is decent).
You would also find Lycans at the Training Grounds, Catacombs. When you reach the Forbidden Grove, these Lycans really get in the way because they've also acquired a taste for the Ancient Cheese. Ouch.
[Jan 2010 above, Oct 2008 below]
The Lycan's wandering around the Mousoleum currently.
If you manage to catch it, it may drop the Shredded Furoma Map Piece. A whole new area opens up and what you currently have is the Training Area. New mice types are there.
Standard Mousoleum strength traps and cheese work on the Lycan. That is, portals and radioactive brie. Some have even had success with the force field trap.
Latest: Lycan are drawn to Moon Cheese!