Can I upgrade from Lite to Premium to keep my notification rules?

Yes. In your WordPress plugins section, deactivate the Lite version but do not delete it, because this would delete the database table which stores your rules. Then upload the Premium version and activate it. On PSN's "Overview" page run the Selftester (right sidebar) to be sure that the database layout is up-to-date. The Premium version uses the same database tables as the Lite version. You will find your formerly used rules in the "Rules" section. To remove the Lite version from your plugins list, delete its directory "post-status-notifier-lite" on your server (e.g. with a FTP tool of your choice).

Refer to the Upgrade Howto for more details about how to upgrade from Lite to Premium version.