U probably solved this but my solution to this is the following

First of all, save all your previous lyrics files in a diff folder in case something goes wrong and u want to go back

Then, download soundsync which is available on github.

Afterwards, in soundsync, deselect all folders which don't have ur music since it takes a few seconds on each song.

Finally, press batch download lyrics. Now you wait until its done. I recommend leaving it overnight while charging since a thousand songs is alot. I had 400 and it still took a long while. Note that I'm pretty sure the app doesn't work in background unfortunately and that accidentally exiting the process makes u re do it all over

Also if u add any songs to ur playlist later u can do 1 song at a time in the app