It's too bad we've all gone the way of the variables. Don't misunderstand me, I own mostly variables and they're a great thing. But for short-range guns they are truly unneccessary.
There used to be a real great scope called a 3X. They are few and far between nowadays. And few of us have experienced them, which is a pity. They were the best on the kind of rifle you're talking about.
As a case in point let me relay a story. Several years ago one of my sons got hold of an old .243. It was wearing an old Weaver 3X. The reticle was a heavy post and horizontal line. We both laughed at it. But the boy was strapped for cash so decided to try it for deer hunting that year. He found it entirely adequate, even began to see advantages to it. As for having only 3X's, he had no problem shooting deer to 300 yds. with it.
The boy eventually got the variable bug and bought a good 3X9. It works well, also. Then Dad (yours truly) needed a low-power scope for hunting deer in the forest with his .45-70. The generous lad gave me the "obsolete" 3X Weaver.
The old scope was needing some attention so I located the fellow down in Texas who refurbishes old Weavers and sent it off to him. He gave it a thorough going-over, even replacing the erector assembly, for $38.
You didn't mention what caliber your lever rifle is but I'd bet you'd be delighted if you could strap my "obsolete" 3X on it for a season. No joke, it's the best short range scope made. That post is fast. It shows up better than any of my "dual X's" in dim light. It's powerful enough for any reasonable shot. I have over a dozen variables, all of good quality. They are Leupolds, Burrises, and Weavers. I even have a Bushnell Red Dot. But for a short-range deer scope on a short-range rifle that old 3X is the best yet. Too bad they're so hard to find nowadays.