There are two possibilities, neither of them especially easy to get right. (First note that if you use any fertilizers or herbicides on your lawn, you are better off just skipping it altogether).
If you let the grass grow longish and then cut it (as opposed to mowing from 3" back to 1 1/2" as you normally would in lawn care) you can "theoretically" put some up as hay. HOWEVER the thing is you have to get it good and dry before storing it (impossible in some climates, challenging in most of the rest), and then keep it dry and with good airflow the whole time it's in storage (easy with *baled* hay or even haystacks of 'proper' hay, but because this stuff will be super short staple you almost *have* to bag it, e.g. in burlap bags, and then any slight miscalculation in initial dryness, or any moisture that creeps in during storage, will really tend to go to town in producing mold b/c a bag of short dried clippings just ends up so *dense*).
Alternatively you can put it up as homemade haylage (ensiled hay). However this requires you to be able to get your bags ABSOLUTELY 100% AIRTIGHT and have ZERO pinholes develop during moving them around and storing them; I have not tried homemade haylage myself but have always heard that you should expect to lose many if not most of your bags (once air gets in, it's ruined). Also, there are discussions about whether to feed haylage to goats (I have no clue about camelids but quite likely them too), as opened haylage bags can culture up Listeria. If you could use up a bag within a couple days that is arguably ok (of course, that's IF you could manage to PRODUCE truly-anaerobic bags).
Pat