The two rival studios have played tug of war over Lawrence recently, with both wanting to get started on the second installments to their respective franchises. Lionsgate are clearly the more urgent of the two, wanting to cash in on the incredible success of The Hunger Games, but Fox got to her first and has an option on her contract that they can enforce in the event of a scheduling conflict. Meaning, even if she's only a supporting player as Mystique but the star as Katniss Everdeen, the X-Men must come first.
The original plan for Fox was to begin production later this year, clashing with Lionsgate's plans to quickly capitalise on their monster hit, a turnaround similar to Liongate's work with their lucrative Saw franchise or how Summit (now part of Lionsgate) handled the Twilight series. Fox holding back is good for Lionsgate, but not ideal, as the Catching Fire studio wanted to hold their cast for a 7 month commitment to the production of the sequel.
The First Class sequel will be directed by Matthew Vaughn, the director of Catching Fire is still up for debate.