Is the lime peeled first?

It's not peeled, and it does soften and sort of candy, as PieceOfLayerCake and sdebrango were saying. It will give the jam a delicious smell, and a little tartness and pleasant bitterness, like a marmalade.

I have not made this recipe but in reading it I would venture to say no, it is not peeled. It's like candied citrus peel it takes on a different texture and flavor when cooked in a sugary mixture and is quite delicious.

I'm going to say no since that would be a pretty important detail to overlook. A 50 minute cook should render the skins soft enough to eat pleasantly, and peeling them will eliminate the lovely citrus oils.