In the examples below, you may want to add some parameters to Get-ChildItem depending on what you're looking for. "-Force" to have it list hidden files, "-Attributes !Directory" to exclude directory names.
I would find the output most useful in a csv.
Get-ChildItem -Path K:\Transactions\Processed\Audit-Images\Lane` 12\$date\done -Recurse | Select-Object Name,LastWriteTime | Export-CSV "C:\2\filename.csv"
Same line, in a text file:
Get-ChildItem -Path K:\Transactions\Processed\Audit-Images\Lane` 12\$date\done -Recurse | Select-Object @{n='File';e={$_.Name + " " + $_.LastWriteTime}} | Out-File "C:\2\filename.txt"