Depends on the kind of grass.

If we're talking lawn fescue, that critter ain't going to gain worth crap, due to all the edophyte contamination. Other lawn-type grasses aren't much better.

But there's lawns and grass and then there's lawns and grass. Here's something I learned this past weekend at the Sheridan Experiment Station:

Orchardgrass and the wheatgrasses (crested, intermediate, pubescent) make for some pretty nice looking lawns. Not as spiffy as the ultra-slick bluegrasses, but then I don't give a rat's rear end for a lawn that looks like a golf course. These grasses, ordinarily used for grazing, when seeded densely enough, made for some nice looking lawns (IMO). And relative to this discussion, these would be perfectly acceptable grazing grasses for a calf or sheep.

On the farm in Nevada, we planted some grazing tall fescue. It never looked worth a darn as a lawn, as it retained its bunchgrass habit.

The new folks have three ewes on that lawn (which is about 1 acre). Now that endophyte-free tall grazing fescue is looking a lot more like a sod-forming grass and it is filling in to create a really nice looking lawn.