You could try spiking the lawn. Depending on your situation, time and size of garden this can be done by hand with a garden fork or hire a petrol spiker. This is to break up any compaction plus aerate the soil. Lawn sand is a moss treatment needs to be watered in after application (follow the instructions on bag.) There is another product Bioacter which does not need to be scarified. Not tried it myself.
Also is your garden shady? this will encourage moss plus cutting too low. Reseed any bare patches.