Yes we thought this but do not have a clue as to why - all we came up with is felt ...felt hat but thought it was rather clutching at straws. What made you think of this - sorry to sound so stupid but just cannot make any sense of the clue.
I have to confess that my only reason was the felt bit, as you said, and lots of litres - ll - but don't know where AA comes into it. The only other word I could think of that fits the letters is maligner which doesn't begin to fit the clue.
We understand AA Milne with r on the end to make Milliner - how come it is lots of litres for li? Why is Li lots of litres. Are we being obtuse - just cannot see this bit.