Christian Benteke, preferred to Darren Bent, put Villa ahead in the 27th minute but the hosts had Joe Bennett sent off for a second bookable offence early in the second half and Michael Turner equalised with 11 minutes to play.
Lambert, who made an acrimonious departure from Norwich in the summer, has overseen just one win in his first nine league games at the Villa Park helm.
The result took Villa one place up the table to 16th, two points above the bottom three, with Norwich one point better off in 15th.
Arsenal will be looking to put consecutive defeats at the hands of Norwich and Schalke behind them later on Saturday when they return to domestic action at home to bottom-of-the-table Queens Park Rangers.
Manchester City also suffered a damaging Champions League setback in mid-week, going down 3-1 at Ajax, and face Swansea City in the day's late kick-off.
Elsewhere, West Ham United could climb as high as fourth with victory at Wigan Athletic, while second-bottom Reading host Fulham and Stoke City welcome Sunderland to the Britannia Stadium.