Options as I see them:
#1 - hard hitting 'big bore'
Lever action in 45-70. Problems - A lot of 'off the shelf' ammo for it is quite tame. Solution - buy very potent loads from a boutique ammo maker or load you own. Problems from the solution: Not everyone is a reloader, boutique ammo is very expensive, and either way the recoil is stiff to say the least
Lever action in 444 mariln. Problems - the cartridge was designed to use the 44 magnum's bullet, which means there are a lot of light weight projectiles, not much sectional density which is needed for bear IMHO. Also, while the run of the mill cartridges are a bit more potent than the run of the mill 45-70, if you get into some of the more premium ammo 45-70 and 444 give very similar energy figures, but the hottest boutique and handloads don't keep up with the hottest 45-70 (not counting the monsters you can reload for a strong single shot). Of course very stout recoil in the hot stuff.
450 Marlin - Marlin intended to give us something where the run of the mill shelf ammo would be equivalent to really really hot 45-70 handloads, with no risk of someone sticking the cartridge into a relic and loosing their eyesight. Problem - rather than basically doing an Akley Improve of the 45-70, Marlin made some odd dimension choices and gave it a belt, so not a super-ideal round. Plus most premium hunting ammo for it is pretty much in line with the premium, real rip-snorting-hot loads aren't very often seen on shelves so in reality the cost and availability isn't much different than a 45-70. Finally, there isn't any 'soft' 450 marlin factory loads for recreational shooting, practice, etc. Of course very stout recoil in the hot stuff.
So what if you reload? Is the 444, 45-70, or 450 a good choice then?
Seems to me if you are going to commit to reloading, might consider reloading something more potent.
While not included on this chart, there is also the 450 Alaskan, which even keeping to the mild limit of 44K chamber pressure, spit out 4,200 ft-lbs of energy.
People started out pairing the 450 Alaskan with the Winchester Model 71, but there aren't many of them left. Now people are using marlins to handle these wildcats.
#2 Hard Hitting Medium Bore.
I'll start out with the BLR lever action and the 325 WSM. This round basically splits the difference between a 300 winmag and a 338 winmag, and does it with a shorter case. This has a significant power and a significant width advantage of the 30-06 which has taken many bear. All around a great gun. I expect it would stop a bear even better than off the shelf 444 and 45-70 ammo, and better than the premium hunting loads, but would be inferior to the hottest boutique and hand-loaded big bores.
The classic lever action medium bore is the 348 Winchester, although it was only ever chambered in one gun...the Winchester 71. Incidentally the Winchester 71 is probably the finest lever action repeater out there, and probably the strongest. This gun and this cartridge are the starting spot for the supremely potent 450 Alaskan mentioned above. The cartridge doesn't have the power of the 325 WSM, but surpasses the 30-06's heaviest bullet with it's heaviest bullet. It would have a slight margin of effectiveness over a 30-06 in a platform that allows faster shots, and overall recoil would be quite similar to the 30-06 but just a tad stouter. Unfortunately, they are no longer made.
358 Winchester - just like the 35 whelen is a 30-06 knecked up to give more short to mid range stopping power than the 30-06 without going to the extreme kick of a magnum, the 358 Winchester is the 308 necked up. Unfortunately, most factory loads for it aren't going to the top of the allowable pressure meaning it's edge over a round like the 30-06 while still present is smaller than it should be unless you are a hand-loader. It's raw energy falls a tad short of the round it replaced, the 348 winchester. Also, not many guns are chambered in it any more, making it almost a de facto used gun purchase.