Welcome to FT!
Sorry to hear about the problems. I would hate to arrive at destination without any bags - I'm surprised that LH made you check-in your hand luggage? They were excessive in size or weight?
Anyway, first of all the response time from LH is much longer than 2 weeks. 6-8 weeks are not unheard of in matters like this. If you have not heard from LH in 3-4 weeks from now call or trying email again - did you receive an email from LH with the case/reference No?
Secondly, if you have original receipts for necessary purchases of clothes, toiletries etc, LH will most likely refund the expenses. I don't expect any issues there (unless of course if the nature of the purchases made or the total amount per pax give rise to objections). However, if you have travel insurance coverage these expenses will often be covered and paid out much more quickly than by the airline so check with your travel insurance also.