The business is moving out of the Palisades Media Group after seven years. It is the second Hollywood loss in a week for the agency following the departure of the MGM Studios account.
Lions Gate began its pitch in June this year, although it is unclear which agencies were approached.
Tim Palen, the co-president of theatrical marketing for the company, said in a statement: "We cast a broad net and spoke to dozens of agencies. We're really excited about the fit between Lions Gate and Initiative and look forward to a lengthy relationship."