If the lump is near the base of your little and /or ring finger, it may be Dupuytren's contracture.  This causes a puckered appearance around the palm fold and a lumpy feel which isn't usually tender.  As it progresses it causes the little and ring fingers to curl towards the palm.  It can also affect the feet, and occasionally the penis (causing a side bend).  If it causes problems in the hand it can be released surgically.  I have tried manipulationg it without success.  It is aggravated by alcohol intake and so is probably affected by vitamin depletion - especially antioxidants.

Other lumps in the palm tend to be tender, e.g. nodules on tendons.

Peter Still, osteopath