Here's how I do it:
1) Configure the LEM appliance to do a daily backup for the logs - archiveconfig option under cmc->manager. This will kick off at 6:25AM daily.
2) Then it's a simple matter of browsing to the network share you configured archiveconfig to point to with Windows Explorer, go into the SolarWindsLEMAlertDBArchive subfolder, and sort by date. Highlight/select the .dat files for the day in question, right click->Properties, and you have the total volume for that day (or more specifically the 24 hours thru to 6:25AM) (note we aren't capturing raw logs in our environment so not sure if those are stored somewhere else).
3) Keep in mind the first time you run archiveconfig it will do a full backup, which could take a while. Subsequent runs will just do an incremental backup, and give you the data storage for the previous 24 hours.