After running apt-get purge lightread, and then trying both logout and reboot, then re-installing LightRead, I am already logged in, as my Google account info was not deleted.
Moreover, manually deleting the data is a bit problematic if you don't already know where the databases are stored, and which databases pertain only to LightRead. The databases are stored in a non-intuitive location ( ~/.local/share/webkit/databases), and there are multiple databases, as well as a subdirectory containing another database, inside the webkit directory, making it difficult to determine which database(s) are relevant to LightRead.
Furthermore, it seems possible that other applications might also follow the same paradigm and rely on this shared webkit directory, making it even more difficult to determine which files/directories can be safely deleted without impacting other apps.
I had to install another program (sqliteman) to be able to inspect the databases, and doing this made it seem that nothing is cleared by apt-get purge and reboot, including feed and article data, in addition to the login data (which appears to be in ~/.local/share/webkit/databases/file__0/file__00000000000000001.db).
It would seem safer if any sqlite databases specific to LightRead are segregated in an explicit LightRead directory under either ~/.local/shared or ~./config (whichever directory is used by the majority of other apps, to make it more intuitive). More explicit file naming might useful too, but if all the files are at least in something like a ~./config/lightread/databases directory, then the file naming is less critical. Manually deleting that directory (if needed) would be less scary, even without installing sqliteman :)
If I recall correctly, there's no way to tell webkit, where to store localstorage/