Correct, the upgrade gives you a seat in C but other conditions of the ticket remain the same.

Cant find the LX equivalent, but LH.com says:

Please note that the fare conditions of your original ticket, i.e. the rules concerning rebooking, refunds and baggage, remain unchanged. Likewise, the free baggage allowance associated with the originally booked Economy Class fare will still apply to the upgraded flights. The allowance is shown on your passenger receipt.

By the way, as HON you get an exception to the no bagage rule on long haul, but not on short haul.