Just a thought...
It is a manual process.....but you can use the Custom Actions Screen to record the Monitor Serial number on each computer in one of the Custom Fields. You can then create a report to query the computer name and custom field. You can even change the it-cust.aspx for the website to change the header from "Custom1" to "Monitor SN" or whatever string you want.
If you are MSSQL savvy and already have the monitor serial number and computername assigned, you could bring that data into the Lansweeper tables automatically if you so choose.