A major Hollywood studio in charge of one of the most explosive action franchises is facing equally explosive pushback. But it’s got nothing to do with any of the movies themselves. Rather, Lions Gate Entertainment Corp. is taking flak for a “first of its kind” artificial intelligence deal. According to the Wall Street Journal, the studio in charge of films like “John Wick” and “The Hunger Games” has inked a major AI deal with Runway, a “fast-evolving AI startup.” The Journal described this deal as a bit of a mutual exchange. Lionsgate will give Runway “access to its content library in exchang…