Came across this practice in Jeremiah Tower Table Manners: How to Behave in the Modern World and Why Bother
Putting cheesecloth or cotton clothes on a lemon is not an affectation but, rather a highly practical courtesy, one that prevents digging for seeds in iced tea, or prevents squirting someone in the eye with lemon juice when all you are trying to do is flavor the fish. It also saves having to remember at formal occasions how to squeeze the half-lemon gracefully against the prongs of a fork.
Had to go search for a picture (basically a lemon cut in half at its equator and the cut end wrapped in muslin or cheese cloth).
And so for day 2375