In our airline L1 has is responsible for the front galley and the cockpit - which means checking that they are awake, providing them with food/drink, ... Before the flight we bring them a plastic bag for the rubbish. After the flight they usually drop it off in the galley on their way out. Whatever we bring up turning the flight (trays for the meal, newspapers, ...) we clear away again before top of descent (or earlier - once they have finished).
It's part of the responsibilty of this position - some people don't like it (and try to avoid to do it), others don't mind - that's why we usually get to choose where we want to work
