Lynn has previously served as the running backs coach with the Browns between 2007-2008, before coming to the Jets as a part of the Rex Ryan coaching staff. He had interviewed for the vacant head coaching position with the Jets, but was passed over for Todd Bowles.
Obviously Mike Pettine is the current head coach in Cleveland and Lynn worked with him as part of the Jets staff, so there is some familiarity there. Lynn seems to be a really good coach and players have always spoken very highly of him, I think he's ready to make that next step and doing it away from the Jets is probably more likely.
I haven't heard Lynn's name mentioned in connection with the vacant Jets offensive coordinator position but he'll have a chance to impress the coaching staff in Cleveland. I'm sure Todd Bowles will want to bring in his own guy as assistant head coach, and Lynn is probably looking for a more distinguished role than just a running backs coach.
The Jets have been committed to the ground game under Rex Ryan and finished 5th in rushing in 2014. The Jets have had a rushing attack by committee approach and Shonn Greene was the last rusher to break 1,000 yards in 2012.