Roasting, in contrast to boiling, solidifies into one single unit the meat of all the parts of the lamb. Since boiling fragments those parts, it was specifically forbidden. The lamb had to be roasted as one single unit. It had to be eaten in one house in the same place and not in two places. It was forbidden to break the bones of the lamb.
Every bone has to remain complete.
The lamb had to be one year old. Its age also symbolises the concept of oneness. The lamb had to be eaten together with the Matzot and the M'rorim. The Matzah represents freedom and the Maror the enslavement, which are two opposite ideas of the same theme. Nevertheless, and because of this, they had to be eaten together, as Hillel later did, when he made them into one sandwich.