Lee took over as Bolton boss after the departure of former Sky Blue Sam Allardyce's move to Newcastle United.
Dowie's family hails from Bolton and with Coventry City facing an uncertain future,a move back to his family home could be tempting if it was to be offered.
"This has been a difficult decision for all parties but we have agreed the time is right," said Bolton Chairman Phil Gartside said about Lee's departure.
"Sammy has played an important part in the club's recent history. We wish Sammy and Frank well for the future. Our efforts will now look for a replacement manager and to concentrate on the future."