I can help. I know this part of the family is on my tree, I've just gone over it for my grandfather, Cliff Lester (descendant of a common ancestor of the Lesters you mention).
I have traced this part of the Lesters back to Plymouth and the Mayflower, and back before that to about the 1300s. Unfortunately it was with OneWorldTree, so the info is only as accurate as its submitters. I've still put in as many records as I could get my hands on in the 14 day free trial.
Please email me if you're interested and I will see what I can do for you.
Any other interested Lesters - send me an email. I'd love to get in touch and find cousins. =D