My first 3 elk were taken with a Winchester 30-30 and open sights. As a kid, I hunted with my Grandad throughout the foothills of the Bighorn Mts. of north-central Wyoming. Grandad did not read much of anything except the local paper. He did not know anything about ballistic charts or energy figures. But he did know a lot about elk and their favorite wallows and feeding meadows. Grandad had several decades of hunting experience with his 30-30 and knew how to shoot straight!
The modern elk hunter armed with a 30-30 carbine faces the same handicaps of 111 years ago. That is, shots much beyond 150 yards or so should not be taken. Grandad instructed me to always shoot twice. This is a fairly easy technique to master with any rifle type; the lever action is especially suited for a quick second shot! Two 170 grain softnose bullets through the lungs will get the job done quite well.
Good hunting to you.
TR