Delon Armitage, returning to Irish's line-up after missing the Heineken Cup defeat to the Ospreys, was sin-binned for a high tackle, before replacement Ryan Davis slotted a drop-goal.
But Toby Booth's men responded with Lamb kicking two penalties, the second just five minutes from time, to hand the Exiles victory.
A late Brett Deacon try gave Gloucester a 33-26 win over Harlequins at Kingsholm despite a valiant fight back from the visitors.
Danny Care's early try was cancelled out by scores from Dave Lewis and Charlie Sharples, in a game in which Nicky Robinson also kicked four penalties.
Gloucester props Paul Doran-Jones and Nick Wood both saw yellow in the second half as Nick Evans' fine kicking gave Quins a glimmer of hope.
Evans, who bagged 21 points in all, then scored with a 25-metre run and converted to level the scores at 26-26, but Deacon crossed over from a five-metre scrum to secure the points for Gloucester.
Toby Flood produced a near-faultless display with the boot to bag all of Leicester Tigers' points as they outfought Bath 21-15.
Olly Barkley kicked five penalties to earn Bath a losing bonus point, who were without Lewis Moody after his eye injury denied him an emotional return to Welford Road.
Despite Barkley's impressive kicking, Flood's six penalties and a drop-goal secured the points for Leicester, who now occupy fifth spot in the table.