It was reported that Fox initially wanted to start production on Days of Future Past
in fall 2012, but pushed it back to January 2013 to accomodate Lawrence's schedule on Catching Fire
. There's this from IFC, for example:
Fans are going to have to wait half a year longer to see the planned "X-Men: First Class" sequel, and it’s all the fault of those darn "Hunger Games."
At least, that’s the case according to The Hollywood Reporter. The outlet is reporting that 20th Century Fox has changed their planned shooting start date for the “X-Men” sequel to accommodate Jennifer Lawrence's filming schedule on “The Hunger Games” sequel, "Catching Fire."
If Fox had wanted to, they could have made Lawrence film the untitled “X-Men” sequel first. She signed a sequel clause in her contract before she came on board “The Hunger Games,” so technically Fox had first dibs. The plan originally was to have the follow-up to “X-Men: First Class” start lensing in the fall, but now Lionsgate is planning for “Catching Fire” to go in front of the camera in August or September. Instead of having a fuss about it, Fox has opted to start shooting “X-Men” in January 2013.