The agency triumphed following a six-way pitch against undisclosed agencies.
It will now work on a brand campaign to promote the Virgin Casino division, with a focus on marketing to 25- to 34-year-old men.
Virgin Games has run digital advertising in the past, but has produced its creative in-house. Ross Sleight, the marketing and operations director of Virgin Games, said the decision to appoint an outside agency was a precursor to increased investment in the medium.
"We have had a consistent online presence, from branding to search, but we now want to increase that by three or four times in terms of media spend," he said.
"It was a close call with one other agency, but Lean Mean Fighting Machine came up with an innovative solution to the brief."
Along with other online gambling sites, Virgin Games is subject to heavy restrictions on the on- and offline advertising of its products.
"Our challenge is to maintain the Virgin attributes of cheekiness and irreverence while staying within the law," Sleight said. "The new campaign will bring a radically different approach to our online advertising."