Remember that in order to sync, a Spotify Premium account is required.
Otherwise, you can as well upload an audio file.
Steps to change your Spotify account on Musixmatch Pro are exactly the same for the desktop version or the app:
Login to your verified artist account on Musixmatch Pro
Select the Roster tab
Select any of the artists
Select any of the songs
Click on Lyrics to open the artist studio (where you edit and sync the lyrics)
Click on More (the three dots in the top right corner)
Select setting
Select 'disconnect' to disconnect your Spotify account
Connect another account