The UK agency has successfully retained the account a number of times in the past.
MEC was reappointed by Lionsgate in 2009 after fighting off competition from Initiative. The business was then worth £12 million.
The agency also retained the account in 2011.
In August last year, MEC brokered a six-figure deal between Lionsgate and Channel 4 for the launch of Sin City 2: A Dame To Kill For.
Recent Lionsgate releases include They Came Together, Love, Rosie and The Expendables 3 in 2014.
In 2012, the Advertising Standards Authority banned a YouTube ad for Abduction.
Lionsgate did not respond to a request for comment.
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