The 33-year-old Lampard struck from the penalty spot in the 44th minute after Salomon Kalou was brought down in dubious circumstances in the box.
Fulham equalised with seven minutes to go when Clint Dempsey headed his 16th league goal of the season from a right-wing corner.
Chelsea remained sixth in the table, two points behind Tottenham Hotspur and Newcastle United, who are level on 59 points with five games to go in the race for the fourth and final Champions League qualifying berth for next season.