as 115grfmj said, ANY rifle will have POI change as the barrel heats up. I have no reason to believe that lever guns are any more or less susceptible to it. Generally speaking, though, lever guns are not necessarily the most accurate type of rifles, for several reasons. If you want a very precise, sub-MOA rifle, get yourself a good bolt action, bed the action and free float a top quality barrel. If you want a light, handy, reliable repeater, get a lever action.
The .357 and .44 magnum lever guns are both excellent guns within their limits. They launch much heavier bullets than true rifle calibers, at substantially lower velocities. That limits their effective range to around 200-250 yards maximum, which also means that slight shifts in POI are nowhere near as important as it is with a high power rifle you will be shooting at 300, 600 or even 1000 yards. Between these two, the .357 magnum (or maximum) will give somewhat higher velocities and lighter recoil than the .44 mag. I prefer the .44 magnum, myself.
As for a heavy octagonal barrel vs. a lighter round barrel, well, I just don't know. Theoretically, the octagonal barrel should be more accurate. It is stiffer, and so should better resist changes in pressure on the stock, etc. It also has more thermal mass, meaning it will change temp more slowly, which should lessen shot-to-shot inconsistency somewhat. It is also heavier, which translates into less felt recoil (and potentially less of an issue with flinching, faster shot recovery, etc.).
That said, I don't know how much it really matters. I own both octagonal barrel and round barrel lever guns. For the kind of shooting I do (hunting, plinking and cowboy action), I prefer the lighter weight and quicker handling of the round barrel. I suppose if I put them side-by-side on a bench and tested carefully, I might find the octagonal barrel to be slightly more accurate over the long run, but I think the difference is small enough to be insignificant compared to the skill of the guy behind the trigger.