If you book a short-haul ticket with Lufthansa or British Airways, you'll almost certainly be offered a range of fares including a "hand-baggage only" fare. This comes with zero included checked bags.

Even if you have elite status with BA, you won't get an free checked bag if you book such a fare[1]. LH are temporarily "as a goodwill rule" allowing their elites and star alliance gold elites to get one free checked bag on 'Light' fares[2].

1. https://www.britishairways.com/en-gb/information/baggage-ess...

2. https://www.lufthansa.com/uk/en/economy-light-fare