I think this is stored within an attribute that Lansweeper doesn't query. The following is a PowerShell script which will give you a list, albeit outside of Lansweeper.
$logLocation = 'C:\Windows\Temp\LogOnTo.csv'
get-aduser -filter * -properties LogonWorkstations | Select-Object SamAccountName, Name, LogonWorkstations | Export-csv -path $logLocation -NoTypeInformation