Are you asking in this Forum for advise, whether TG will help you to cheat LH on the luggage fee and expecting other Forum members will report you experiences from their "cheating practices"?
usually TG will check through luggage for LH on different tickets (I have experience in that but with tickets with enough bag allowance), but they will only do if they see the luggage allowance on your ticket. If the check in agent makes the mistake to check through your luggage, then they will collect the fee before Boarding in Europe or worst case your luggage will not make it to the final destination if they feel they have not enough time to collect the fee
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