Okay, so not a disk full. It appears that the database isn't running on the LEM, so events aren't getting archived. Your temp space is being used to store events while the manager collects events with no place to put them. Eventually, that's going to be full and the LEM will start rotating that space, which will lead to gaps in the logs.
Now, it looks like you have an older LEM version (5.5 or prior), but I'm guessing from the size of the partitions this is a virtual appliance. Since it's unlikely that you did an L4 deployment (separate database and manager appliances) in a virtual environment, it sounds like the database on the LEM has stopped for some reason. You really should open a support ticket so we can try to repair the database and get it running before you start dropping data.
Once it's fixed, you should move to 5.6 and then 6.0, which will mean migrating to the new database standard for the LEM.