My husband has a CR-1 visa and his green card which is good for two years. he is able to travel out of the US right now and has done so. However, I heard somewhere that once we file to lift conditions they will tell him he cant travel out of the country for a certain amount of time. Does anyone know if this is true and for all how will travel be restricted?

There is no restriction on travel during the lifting conditions... he just needs the NOA1 extending his greencard for 1 year and his expired greencard and a passport...

Kez

Regardless of lifting of conditions, there is ALWAYS a risk of being deemed to have abandoned LPR status if a Green Card holder travels out of the US for a long time. Normally, trips of less than six months aren't a problem. Beyond that, see the rules regarding reentry permits and such.

Filing the I-751 does nothing to change this issue one way or another.

When you file the I-751, there's a chance he'll be called to a USCIS facility for an interview and/or biometrics. There can be some logistics issues meeting their requirements if he's so far away that he can't reasonably show up when asked. If nobody is checking mail, he may miss an appointment notice, which can be a bad thing.

But there's no explicit restriction on travel during the process of lifting of conditions.