Morgen Alpenrose -

1. I do not know of a "gate delivery" service offered by LH Worldshop at FRA.

2. For years I took the tram from FRA into town, doing business at the LH Worldshop there, and the returning back to FRA. Now that there are LH Worldshops inside FRA, it is very much easier to complete business, and save time in the process.

3. 2 carry-on/IATA-size cases onboard ? Perhaps in Business or First, and perhaps not.

SOLUTION:
It is possible. I did this twice, but pre 9-11 when luggage requirements were more relaxed onboard. LH, Condor, Swiss, Alitalia, Varig, even Air Dolomiten were more accommodating then with extra carry-on. Today, no longer.

What I could suggest to make this happen is to contact the airline ahead of time, and explain your intentions. See what they say, as this is a common occurrence enough at FRA. I would think that such a purchase could be inspected and processed, and then 1 could be checked, or even gate checked, given enough time.

That success of this purchase would be predicated on:

1.) Paying for the items ahead of arrival ( As I have done many times to ensure it is held and waiting in stock whenever I arrived ),

2.) Allotting then enough time to make the pick-up in the airport, with

3.) Inspection and documentation processing as a customs export,

4.) New cases then checked, or gate checked.