When we did our grass (refuse to call it a lawn) I just added the moss and dead grass etc. to the compost heap. Did mix it up with a load of other stuff though. It seems to have all rotted down. Theory is that pure moss will not compost, or only do so very slowly, but we have never had any bother with it.
Unless there was a broadleaf weedkiller in with the moss killing stuff, in that case then yes get rid.

Wow Hank, is it really three or four years ago??

Just looked back, S, April 2011 ! 5 years ! Similar to yourself I think.

Hi Hank, yes I agree with Owdboggy, a long time ago I raked a load of moss out of my ''lawn'' and just left it in a heap on its own, 2 years later it was still there only lightly composted in the middle of the heap, but mixed with other stuff on the compost heap it seems to rot down fairly quickly, just don't overdo it, Derek.

Lol Hank , it doesn't seem that long - yes, just two months after me then...

Thanks Derek, but had your lawn been treated with moss killer ? If so, it's going on the compost heap tomorrow.

Ours had been and we still added it to the heap. Actually added stuff when we used Lawn weed killer too, but our heap is not going to be used for 2 years so the toxicity has gone by then,

Thanks OB, will add it in layers as it won't be used for a couple of years similar to yours.

Oh dear all of us having to treat our lawns, mind you it makes me feel so much better knowing I'm not suffering alone, I try and rake as much out as possible before treating the lawn, its hard work and boy I swear but I then use my pile to decorate some of my baskets with when its planting up time, recycling I call it, lol....

I think there will be record quantities of moss this year after all the rain.