A fine header from veteran France forward Olivier Giroud put Chelsea ahead in the 34th minute at Stamford Bridge, but Dutch forward Anwar El Ghazi equalized early in the second half.
Villa went close to a second goal when midfielder John McGinn hit the crossbar in the 69th minute, but Chelsea left-back Ben Chilwell almost grabbed a dramatic winner deep into injury time when his superb volley from wide on the left fizzed just past the right post.
The draw keeps fifth-place Villa one spot ahead of Chelsea on goal difference and one point behind fourth-place Manchester United, ahead of Friday’s trip to Old Trafford.
Lampard selected Giroud ahead of Tammy Abraham as he continued to rotate his central striker, having chosen Abraham in Saturday’s 3-1 defeat at struggling Arsenal.
Giroud started and finished a move for his ninth goal in 15 games overall this season.
He received a pass with his back to goal, then fed Christian Pulisic with a deft flick and Pulisic instantly played the ball down the left flank to Chilwell. His quick cross was slightly low, but Giroud adjusted his body to twist and meet the ball with a thumping header into the bottom left corner.
Poor defending gave Villa a soft equalizer, as El Ghazi was left alone at the back post to volley in a right-wing cross from Matthew Cash through goalkeeper Edouard Mendy’s legs.
Moments before McGinn's superb shot, Chelsea captain Csar Azpilicueta found the net from close range, but his effort was ruled out because Pulisic was offside when taking a shot seconds earlier.
Lampard brought on Germany forward Timo Werner for Giroud to give Chelsea’s attack extra pace for the closing stages.
But it was Villa who threatened more, and when striker Ollie Watkins headed the ball down for substitute Jacob Ramsey in the 82nd his curling shot from outside the box went just wide.