The Scot had guided Villa to 10 points from their first four matches, but five successive defeats without scoring a goal have resulted in the pressure building at the West Midlands club.
Lambert's opposite number Mauricio Pochettino has also faced criticism for recent displays from his Spurs team.
The North London outfit have performed well in cup competitions, but three defeats in five league contests is something that needs to be addressed by the Argentine.
Striker Harry Kane is knocking on the door for a league start after scoring four goals in matches with Asteras Tripolis and Brighton & Hove Albion respectively.
Aston Villa: WLLLLL
Tottenham Hotspur: DWLWLW
Possible starting lineups
Aston Villa: Guzan; Lowton, Vlaar, Clark, Richardson; Westwood, Cleverley, Sanchez; N'Zogbia, Agbonlahor, Benteke
Tottenham Hotspur: Lloris; Naughton, Kaboul, Vertonghen, Rose; Dembele, Mason; Chadli, Eriksen, Lamela; Kane
Sports Mole says: 1-2