The Connect is one of three phones based off of the LG Cayman AS840:
LG VS840 Lucid - Has CM10 out
LG LS840 Viper - Has an unofficial CM9 port that doesn't work, don't think it even boots up, and it looks abandoned.
LG MS840 Connect - CM10 based off of Lucid build.
If CM7 existed for any of the Cayman phones it could be probably be ported. The Viper CM9 could be a possibility, just need somebody to play around with it.
AS840 is in archived devices here and doesn't look to have any development whatsoever. I do have AS840 firmware on my computer tho LOL...