When App Lounge first opens, I am fairly confident, the exchange of tokens starts and one sees an animated blank screen. I take care that this clears within < 5 seconds and detail of apps and individual apps succeeds before proceeding. This is on the basis of my belief that token exchange failed so any install will fail.
The FAQ very importantly includes the advice to Clear storage and to WAIT.
Clear App Lounge’s data by navigating to Settings > Apps > App Lounge > Storage & cache > Clear storage, then wait for a while before you use the Anonymous account login again.
Please be prepared to wait say 12 hours in order to clear the remote server of the memory of this fail to deliver to a compromised device. Also it is a good idea to have a well charged battery as this gets checked before delivery and install starts.
While Google email login is supposed to work I never used it and there may be some Google login bug at present. Possibly related Release v0.3.13.250932 · microg/GmsCore · GitHub.
You might consider whether Anonymous login is satisfactory and just Google login the fail.