Sorry for the late reply its been a busy few weeks.
It depends if your also using the Encrypter or not. Out of the box Laravel uses it for secure cookies. So sessions would invalidate.
If you also use it then anything you’d encrypted couldn’t be decrypted using the new cipher key.
I think we use Laravel 4 on PHP 7.1 on one of our work projects but I think thats running fine. For some projects when we last upgraded our servers we only did it to PHP 5.6 as we had issues with Laravel handing ErrorExceptions. Which I think Taylor fixed.