After updating LP and rebooting (so that the module for XPosed would be enabled again), both Google accounts claimed that they needed to be re-verified. While the phone was connected to WIFI, the phone was unable to access the accounts, unable to log into them. Switching to mobile data in principle it worked again, until it was switched back to WIFI.

By completely disabling the LP module for XPosed, everything is perfectly back to normal.

I don't want to be rude, but is the LP module acting as MiTM, trying to somehow access our own account, and Google drops the connection?

Has it happened to anyone else? I have checked it in two different devices with the same result