Charlton played the majority of the lacklustre Home Park contest a man down after goalkeeper Nicky Weaver was sent off in the second minute for deliberate handball.
Argyle made the break-through on the hour when Jermaine Easter latched on to a header from Gary Teale to score his seventh goal of the season.
But their lead lasted just five minutes as Lita headed home the equaliser.
Charlton did go in front 15 minutes from time when Lita grabbed his second of the game after a neat link up with strike-partner Chris Iwelumo.
The result lifts Charlton to eighth, a point behind sixth-placed Wolves, although the Addicks have played two games more. Argyle are a point back in ninth spot.