OP, I only use pistol cartridges for hunting these days. Generally same loads work fine in pistol or lever action. I will add the caveat that at the extreme end of low loads for pistols you can get bullets stuck in the barrel of leveractions as the small charge and friction of the longer barrel can actually cause the bullet to stop. These are usually experimentally slow loads( like cowboy action shooters may use), not regular load manual loads. At the other end chasing the highest velocity with the heaviest/slowest powders, while folks say after 18-20" of barrel you dont get more velocity gains, fact is with some powders you can keep gaining until 24". We are talking the heaviest safe loads of stuff like 110 or 300MP in the strongest 92 actions. But those two extremes aside, just use any book load in pistol or lever action no probs.
I see there being 3-4 load levels in 357 and 44 mag
1. plinking or subsonic load levels. This is usually 3-5 grains of something( the fastest burning powders on the chart. Stuff like bullseye, win231, Clays, red dot, etc), often with lighter or cast bullets( heavy jacketed bullets will generate more pressure/need more powder due to the increased friction in the bore) These are fun plinking loads but in 44 in particular still have some thump at close range. I use light loads like this with 240 cast bullets for medium size pigs at night to 50 yards over baits where I need to keep noise down. The realities are you may get 80-150fps gain going from pistol barrel to lever actiion barrel length here as that light charge is burnt up pretty quickly, or no gain at all.
2. What I call my "9mm carbine or original 44-40 load" levels. I dont use these calibres its just a comparison to the equivalent speed in 357 or 44 mag lever actions. This is just into supersonic speeds, 1200-1350fps. (Roughly what 9mm carbine bullets do and the old 44-40 original velocities). This is fairly low blast, low recoil but suprisingly a good killer within its a range limitations. Powders for this can include the faster powders above with slightly heavier( load book safe) charges, and you can also start using loads with the slightly slower powders, what I call the mid-burners. These are the next level in slowness in the load chart, things like Unique, Universal, etc. Loads may be 6-8 grains or so( ballpark figure). You will find decentish gains going from pistol barrel to rifle barrel with these slower powders. Sometimes I have gotten 150fps, some powders the jump was a surpsinging 350fps.
3. Sub-magnum loads. These are basically a magnum load but just not top level. I dont use this often, but it is handy if you have certain powders on hand and want to use them up. This can include heavier charges of the mid burners above, or regular charges of powders slower on the chart like Blue Dot
4. Magnum loads. THese are your regular charges of magnum powders like 110, 2400, 300MP, lilgun.
Again just how I view it. The problem when you write a lengthy post on a subject you leave yourself open to context issues. Some fella will say waitaminit, you said Blue dot is sub magnum but dang thats my magnum powder, or why did you list Win 231 with bullseye when its probably closer to Universal(!). I'm just putting things down a beginner might find useful without bogging the post down with disclaimers and caveats. Hope it helps.