Yea my palms aren't red so I am pretty sure it isn't that; but hey who knows.
You're not going to like this, but I just developed some lines like you've described. I know what's causing mine, I have worms, filiaria, in my hands, didn't have the lines until the things moved into my hands. Might not be what's causing yours though. The baby worms, aka microfilaria, are so tiny they just look like a buildup of fluid in your hands. They are able to go in and out of your bloodstream via capallaries and my palms and fingertips are red.
Welcome. Sorry but I haven't heard of this as a symptom of Lyme, but Lyme and other diseases that often come along with it have variable symptoms in different people and in the same person over time. Post back and let us know when you figure it out! Best wishes --