The Pilgrims, looking to move further away from the relegation zone, fell behind after 34 minutes at St James Park when Liam Sercombe opened his account for the season.
But the visitors hit back and levelled through Lennox with 17 minutes to go before Maxime Blanchard saw red late on.
The deadlock was broken against the run of play. Danny Coles played in Sercombe and his shot from 25 yards and the ball took a slight deflection before nestling in the bottom corner.
Jamie Cureton had a great chance to double the Grecians' lead when he latched onto a poor back header, but with only the goalkeeper to beat, he side-footed high and wide.
Carl Fletcher's side dominated the second half and deservedly pulled level when Lennox's shot took a deflection and went in off the far post.
Argyle were reduced to 10 men when Blanchard was given a second yellow card two minutes from time, but they held on for a deserved point.