Lever guns are hard. The barrel band/handguard make for inconsistency. As for cold bore, one should only really look for it, all else being equal. That is same ammo, temp, bore fouling, etc.
My hunting rifles, I pretty much sight them in "cold bore" since 95% of all big game animals I have harvested were 1 shot, cold bore. Then look for the drift, if any, at 3 and 5 rounds.
For match rifles, I do my best to eliminate cold bore shift, and for the most part, with free floated barrels, knowing my powder sensitivity, etc, they don't have any cold bore shifts.
One thing folks who live in humid climates don't account for is moisture. A fouled bore will have some moisture in it, which is basically gone after 1 round. That can result in a slower, or faster first round depending on parameters.
Also, with semi-autos, many will have a 1st or last round different POI than the rest of the group. Those are easy to determine and adjust for, per rifle, if you are a good fundamentals shooter.