I do the same as Duncan and use different laps for different polishing agents. They live on those plastic office trays meant to store A4 paper, they stack on top of each other and stop on a shelf in a cupboard.
I used to use WD40 before someone on this forum said baby oil was good with diamond, I agree with that and used it ever since.
I have three liners for the inside of the pan, one for normal use, one for 3000 grit and one for polishing.
As I mentioned before every time I touch anything with 3000 grit on it I wash my hands.