I've owned a few lever-action rifles and hunted with many folks who've had them. They're fast for follow-up shots, but most have combs that are too low to align the eye with a scope or red-dot, unless a cheek pad is added.
Almost all lever rifles must be cocked before firing and de-cocked after loading. I've seen a few accidental dischages when the user attempted to de-cock with gloves on. I've also worked on the older models that have had the half-cock notch broken off when the hammer was inadvertantly dropped on it. Another problem with half-cock notches is that it's possible for the hammer to rest on top of the notch instead of seated properly. I had an accidental discharge using a flat-top Ruger S.A. handgun due to that problem.
There are other problems associated with external-hammer rifles, including getting tree spills, dirt, water, and ice buildup on them or in their openings. In cold November weather in Maine, I've found the exposed metal parts very cold, even with gloves on.
As a gunsmith, I've cleaned many Winchester 94s, Marlin 336s and other lever guns and found that many owners never take them apart to clean them. Grit and congealed oil eventually causes parts to wear out or become very difficult to operate.
The Browning lever-action has few of the problems mentioned above, but the trigger pull is usually not as crisp as that of a bolt-action, and they're usually not as accurate, due to the method of fastening the forend to the barrel. That said, they're a fine, modern lever action that will often shoot better than 2 inch groups at 100 yards, depending on how the forend is rested or held. The mechanism is relatively easy to clean and the safety mechanism is very good.
If you decide on a BLR, the .308 cartridge is one of the best for woods hunting out to 200 yards, or so.