You should be able to access the Lufthansa Business Lounge if your TG Gold status appears on your boarding pass.
If you are checking in at FRA then you can always ask for a Lounge Invitation at the check in to make sure you'll be able to get inside !
But if your Gold status appears on the BP there should be no problem : I once forgot my LH SEN card, and wasn't allowed to get into the Senator lounge but was allowed to get into the Business lounge.