I have not played fallout 4 in a while, but for some reason, mouse lag was still a problem as it was in fallout 3 and New Vegas. The fix is the same though. Navigate to here:
Use your favorite file editor to modify these two files: Fallout4.ini and Fallout4Prefs.ini If you do not have a file editor, try notepad, or get yourself notepad++ to enable yourself a lot more editing functionality.
You want to change line iPresentInterval=1 to be iPresentInterval=0
That resolved it for me, again. At least the fix is consistent!