I've found that despite Lansweeper scanning for and having knowledge of "critical" events (they can be seen in the Event Filter widget), they're ignored when it comes to email alerts (I've set one up for a specific ID and source).
It is true that when creating the alert, the event that I'm interested in isn't included in the list (so I had to add it manually), but it should have been there since how else could the Event Filter widget know about it?