The FA decided to impose the fine after The Lions failed "to show an improvement in its disciplinary record" in addition to having yet another "poor record of misconduct" last season.
A further £30,000 fine could be imposed should matters on the pitch failed to improve sufficiently this term.
The Lions' disciplinary record has been poor of late, with the club fined and warned about the conduct of their players on more than one occasion over the past five seasons.