While I don't hunt exclusively (or even mostly) with iron-sighted lever rifles, I use irons enough to have taken quite a bit of big game with them over the decades--and not just with lever rifles, but single-shots, bolts, a double rifle, and a couple of drillings.
Jeffrey noted earlier that big game doesn't need to be perfectly clear to kill it with irons. But many older hunters assume it does, they reason they THINK they can't shoot irons anymore. But the only part of the 3-part equation (rear sight, front sight, target) that really needs to be clear is the front sight, and most of us can handle that, even when 50+ years old.
The last animal I took with open sights was a Texas pig in 2014, a few days after I turned 62, using a Winchester 94 .30-30. But I generally use aperture sights. The longest shot I've attempted was 350 yards on a Quebec caribou, with an old steel Lyman aperture sight and factory front bead. Yes, the bead "covered" the caribou's chest, but at 350 I knew the bullet would land in the middle of the bead--and it did. (However, I cheated somewhat on that shot, however, using a pre-'64 Model 70 in .270 Winchester with 150-grain Hornady Spire Points.)
While pretty small groups can be shot even with relatively crude irons, one of the things that many hunters who've never used irons (or haven't since they were a kid) often have to get used to is that sub-inch, 100-yard groups are NOT necessary to kill big game, even at 300+ yards. That .270 wouldn't group any better than 2" at 100 with the factory bead.
