The home side ran in four tries on Sunday as they withstood a late comeback from the visitors to claim a 32-15 victory.
Lamb scored a second penalty of the afternoon on 23 minutes, while Worcester finally got off the mark with a kick from Ignacio Mieres with six minutes left in the half.
However, Leicester landed a significant blow on the stroke of half time when David Mele's try was converted by Lamb to make the score 18-3.
Lamb added the extras to Jordan Crane's try at the start of the second period to keep the scoreboard ticking over for the hosts, but Worcester kept themselves in the match with an hour played as Mieres converted Chris Jones's try.
Josh Matavesi then went over for the visitors with 15 minutes left to reduce the gap to 10 points, only for Mieres to miss the conversion.