Have no solid explanation why the rpms rise other than if you're not using the choke to start a "cold" bike, it may run at a lower rpm until it warms up some.
As it doesn't change idle once it is warmed up, straight or leaned, I'd wadger that's the reason.
Your comment about the handle bar location when you lean it over would lead me to suggest make not sure that's not playing a part. It's not unheard of for the bike to die when the bars are turned full right (or left)
There are several remedies as far as "hot starting" problems go, so you might want to look those up if this is a common issue with your bike.
Generally it's just a safety concern not shutting off the bike before leaning it over on the stand, or backing it up. Same goes for starting off if you're not just waiting for the bike to warm up.
I'd check the function of the clutch switch (while upright on the bike) as well as the handlebar positioning.
The reason I mentioned water in the tank, is because when I worked at a shop a guy came in and showed us every time he leaned the bike over on the stand, the engine would sputter and die. Turns out there was some water in the tank that would flow into the petcock pipe when it was leaned, but wasn't high enough to do it when the bike was held up straight. Kinda doubt it's the cause of your problem, but had to put it on the list.