If your neighbour meant s/he'd get the hay made and take it away in exchange for a couple of freezer-ready lambs, I'd say that's a very fair offer.
Otherwise, ask around local horsey people where they buy their small-bale hay. Find that farmer and ask him/her if they'd like to take a crop of your field
You should get close on 400 bales off 4 acres, that's worth his/her time to work, provided you aren't too far away.
Did your vendors indicate how large a cheque you should expect?
We calculate it would cost us £2 to £2.50 a bale to make small bale hay if we charged for our time, equipment and consumables (fuel, string) like contractors would. Then depending on how far away the farm is, there's travelling time and fuel too - and hay needs to be cut, worked several times, baled, and transported home - so that's a lot of journeys.
Hence I wouldn't expect a huge cheque - which is why I'd say a couple of freezer-ready lambs is a fair offer.
I'd also ask your neighbour if he'd like to put a few sheep on it once the grass comes back to put some fertiliser back in the ground - as Steve says, if you continually crop but never feed, the crop will get weaker and weaker as time goes on.