The only way the lower lats fire is in Pull ups……..so, if you have been doing a lot of pole holds and pole ups—that would be why the Lats hurt.
I would try some "active" rest to help flush the lactic acid from the muscles. If you have a low tension resistance band, or very light free weights(cpl of cans of soup would do the trick) Go through the range of motion of a Lat Pulldown.
Make sure you have done a warm up…..muscles need to be warm……complete a few sets of Lat pulldowns—gauge completely on how it feels. If it hurts right away—stop and rest them for a few days. If this should happen….just soak in hot baths and stretch the Lats gently.
If you have had a proper amount of muscle rest—like the last 36-48 hours, the "active" rest can alleviate the lactic acid from the muscles. If you have been training on the pole like a madwoman, rest. Bath. Stretch. Do the active rest in a day or so.
This would be the most likely cause of sore lats.
The other may be improper form….but I know you are taking Veenas Lessons and she is impeccable about paying attention to details….like correct anatomical position. So, it might be an injury….but more likely, your Lats are just mad at you.
As for the starting on one side and heading to the other….Are you doing pole holds and pole ups changing which hand is on the top?