Lansweeper doesn't search for file types with its scans.
You would need to create something like a deployment package that you run on each machine which checks the machine for database file types saving this information into a network share, you could then look through these files to see what access database files exist, then query. It's manual but could be done.
dir /s C:\*.mdb /b > "\\NETWORKSHARE\Logs\%COMPUTERNAME%.txt
You would need to look for both file extensions though mdb & accdb noting that mdb is used by other applications as well, not just access databases.