Lockjaw caused by aligners. Will it ever go away once treatment has finished?

Immediately see the orthodontist and have them unlock you, if possible,  The trays can be modified to prevent locking by adding occlusal stops .  The longer you wait the more problematic it can become.Are you locking on one side or both?  Are you getting severe headaches.  

Your problem is not an uncommon one as any dental procedure, including orthodontics, can trigger an existing problem that perhaps wasn't identified or fully evaluated before treatment. Clicking and popping are signs and symptoms that the cartilage disc is damaged and partially displaced. What has likely happened is that one(likely) or both (not likely) became completely displaced as the aligners changed the bite you had become accustomed to. It happens even in the best of circumstances and it's not easy or predictable to unlock  these discs in this situation but it can sometimes be done. As the previous doctor advised, first inform your orthodontist and if they don't know how to address this you'll need to find someone who can and the sooner the better or the lock is likely to persist. Most often we will want to also image these problems with both CT scans and MRI so we know the status of both the bone and the cartilage and then can provide a prognosis for treatment.