How would I add "overall provisioning status" to the output of this script?

OverallProvisioningStatus is attribute for Get-MsolUser, so you need to make sure you are connected to WAAD as well. Then, you can do something like this:

OverallProvisioningStatus = (Get-MsolUser -UserPrincipalName $mbx.UserPrincipalName).OverallProvisioningStatus

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OverallProvisioningStatus is not that reliable imo, you can use SKUAssigned instead. Well, depends on what you are actually trying to achieve :)

Thank you Vasil...

So would it look like this?

# The Output will be written to this file in the current working directory 
$LogFile = ($(get-date -Format yyyy-MM-dd) + "-litholdRESULTS.csv")

# Run Script to Set Holds
$MBXs = Get-Mailbox -ResultSize 50 -Filter {LitigationHoldEnabled -eq "False"}
$(Foreach ($Mbx in $MBXs){
Try {
$Mbx | Set-Mailbox -LitigationHoldEnabled $true -ea STOP
New-Object PSobject -Property @{
       Mailbox = $Mbx.DisplayName
       Status = "Success"
}
}Catch{
New-Object PSobject -Property @{
       Mailbox = $Mbx.DisplayName
       Status = $_.Exception.Message

OverallProvisioningStatus = (Get-MsolUser -UserPrincipalName $mbx.UserPrincipalName).OverallProvisioningStatus
}
}
})| Export-Csv $LogFile -nti  

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Vasil you rock!