Sudden Fallout 4 Weird Menu Lag, Workarounds, & Discussion 

As an add-on observation, that same "hit the Xbox button and the lag snaps out of it" thing I noticed for save menus etc. also seems to work in the mods downloading. Left alone, they stay queued for awhile and download very slowly, but once I start a download, if I hit the Xbox button and leave the overlay up they download at normal speed. The minute I close the overlay they lag again. So I got in the habit of hitting download and bringing up the overlay until they finished, and move on. Very weird, but thought I'd put it out there in case it helped anyone else.

Delete some save files and make sure the drive the game is installed on has enough space and is decently fast(not completely full), ive messed around with UI in fo4 before, make sure the your system has enough memory free (the game will stutter if it has to constantly reshuffle the memory to get a task done), ensure nothing is taking up a bunch of CPU time (fo4 is pretty CPU bound), also its worth nothing cloud saves are synced before the exe is even launched, steam does that in the background, the game will only check bethnet when launching the game initially and when in the mod page, GPU memory is also another thing to note, update drivers, there are so many thibgs that influence how a game runs but those are the most common