Chelsea grab comfortable win
Lampard, who switched to west London from east 12 years ago, rose to meet Eden Hazard's dinked ball and head past goalkeeper Jussi Jaaskelainen in the 19th minute.
The 34-year-old midfielder, who has not been offered a new contract for next season, is just two goals behind Bobby Tambling's Chelsea record of 202.
Chelsea went further ahead five minutes into the second half when Hazard completed a neat interplay with Juan Mata.
With Tottenham losing 1-0 to Fulham, Chelsea moved a point ahead of the north London club into the third Champions League qualification place.
While Chelsea eased off when two-up, the hosts were also repeatedly thwarted by Jaaskelainen's agility. The east London club rarely looked like emulating its victory in December just after Rafa Benitez contentiously took charge of Chelsea.
The animosity toward Benitez has cooled, publicly at least, with the interim manager enjoying a day in which only the opposition fans taunted him.
Benitez's job before vacating the Stamford Bridge hotseat in the summer is to ensure the team is back in the Champions League next season.
That is looking more likely, with Arsenal five points back and Chelsea playing with the flair and confidence that was evident in the opening weeks of the season before the collapse that cost Roberto Di Matteo his job.
Chelsea needs its strikers to be more prolific, though. Fernando Torres hasn't scored in the league in three months, and Demba Ba just twice in the league since arriving in January.
Ba was presented with the perfect chance to score after five minutes but couldn't connect with Mata's cross as he stretched out.
An even better opening was squandered two minute later when Lampard pumped the ball through, Ba ran onto it past James Collins but clipped the shot well wide.
Collins himself rifled over in a rare threatening moment from West Ham before Ba turned the ball wide away and Jaaskelainen palmed away Mata's shot.
After Lampard reached his milestone, Andy Carroll had an equalizer ruled out three minutes later when he was adjudged to have fouled David Luiz in the buildup.
Carroll tried again to level, rising to meet Matt Jarvis' cross but he glanced the header wide to miss out on adding to his three goals at the club during his loan spell from Liverpool.
Jaaskelainen continued to prevent Chelsea strengthening its advantage, turning Luiz's low free kick round the post, collecting Hazard's shot and denying Ba with an outstretched left leg when they were one-on-one before half time.
After the break there was little the goalkeeper could do to prevent Hazard scoring.
Mata chipped the ball forward to hazard, who brought it down on his chest, cut past Winston Reid and struck with his left foot into the net.
The game was won now, although Lampard searched for further goals to reach the club's scoring record. The closest he came in the second half was when the sting was taken out of a free kick by a deflection.