Moss is normally removed from lawns by scarification (vigorous raking) in the Autumn if they contain a lot of thatch or in the Spring if only a light scarification is required to prevent the build-up of thatch. The moss removed from the lawn can composted.
However, moss is slow to breakdown having a high lignin content and it may be three years or even longer before there are no recognisable pieces of moss left in the bin. It is therefore suggested that it be composted in a separate “moss compost bin” .
In a revised page on carryoncomposting.com different techniques for composting moss are considered Composting Moss