I suggest the people who think the 88 is the most accurate lever never owned a BLR, but I could reasonably be accused of bias in this regard.
I would be hard pressed to come up with an exact count, but have certainly owned and shot over a hundred lever guns:
half a dozen Winchester 88s in .308 and .243
several Marlin 1894s/1895s (.44 Mag and .45-70)
many dozens of BLRs in pretty much all of the chamberings
several dozen Marlin 336s/30ASs/etc mostly .30-30 and .35 Rem
many dozens of Winchester 94s and 1894s in pretty much all of the modern chamberings and a bunch of the obsolete ones
many dozens of Savage 99s and 1899s in all of their chamberings (I think)
miscellaneous lever guns in rimfire chamberings
probably others that I am not remembering right now......
ON AVERAGE, the BLRs are the most accurate of the bunch. But of course, individual rifles can be excellent shooters even though the model is not noted for accuracy. Example: I have a Savage 99EG in .250 Savage that does shoot three into less than an inch at a hundred yards.

But for Savage lever guns, that is basically unheard of.
I have no opinion about lever guns chambered in pistol cartridges, since I have only owned a few of them and basically considered them to be toys - I did not load for them, for example, nor take them out for serious range work. Barrel heating will be a function of many factors including (most importantly) WHAT LOAD is being fired. Max loads in a .44 Mag will very quickly produce a barrel that is too hot to hold, and BTW is not conducive to long throat life..........
Doug