The whole focus of Passover was the sacrifice of the Paschal Lamb (which is very different than the other Temple sacrifices and unique among Jewish holidays). So the idea is to make clear that, absent the temple, the sacrifice is no longer being eaten. There are different customs about not having roasted anything, or any lamb, but the one universal is not to have roasted lamb. I think there is at least some Sephardic community or communities that have the custom to have lamb as a reminder of the Paschal Lamb, but to make it in an obviously non-roasted way so as to make sure there is no confusion. I think most Ashkenazic communities don't have any roasted meats at the seder (including poultry), so they would add liquid to the roasting pan if making that kind of dish.
Edited by dopey - 4/5/12 at 1:15pm