IMO lever action guns tended to be associated with deep woods hunting due to , well, most are smaller, shorter, hold more rounds of ammo, were cheaper back in the day, making them more common
BUT the fact is, IMO< many folks that hunted deep woods, wandered about till they JUMPED a deer, and then the lever guns were fast to shoulder, again held a bunch of rounds and folks took a LOT of shots at RUNNING deer, so they wanted a FAST reloading gun that held a bunch of ammo!

these days, MOST hunters don't shoot at running deer, its NOT a great thing to do for a ton of reasons and safety being at the top of the list IMO

so, lever guns sort of lost there fame, as some had some safety issue's , and many were NOT as accurate as bolt actions, and not a lot of lever giuns came in LARGE calibers, that a trend of folks seemed to all want Magnum caliber rifles that shot more accurately and farther!
BUT the fact of the matter is, ANY rifle is fine for hunting, deep woods, and almost any place deer live
as long as you can shoot it well
99% of deer are taken with 1 shot , the FIRST shot, so as long as that one gets to the target correctly, there is not need for guns to hold large amounts of ammo, and any gun you spend time with, you can learn to reload it FAST if need be!
practice is what makes one a good shot, not BUYING things!