Every phone has some lag. The Note 7 does slightly lag more frequently than my htc 10 on normal situations.
However I use my phone as navigation while fast charging in direct sunlight on my dash. In this scenario, the htc 10 battery got to 130°F after about 10 minutes and very very heavily throttled performance. The Note 7 in similar situation got to 105°F yesterday and lagged very little after this usage.
Personally I would rather deal with the slightly more lag on my note 7 in normal usage but doesn't overheat when being used as navigation.
This is important to me since I am currently in the market to replace my aging GS4 running 5.0.1. I use my GS4 with Waze and Google Maps (sometime running concurrently) all the time. My GS/4 sometimes chokes on the load and crashes. It can take 3 to 5 seconds to change apps at times. There are times when I don't know if the phone registered the tap and is being slow to respond or if it missed the tap altogether. I call that pretty serious lag! And I often see messages telling me that Weather has stopped. Or that Nova Prime has stopped, etc. (but everything still seems to run normally even after those messages.). Go figure.
It would probably help if I did a FDR, but I see no point in doing that and spending all the time to reload and tweak my apps since I'm looking to upgrade the hardware anyway.
I'm tempted by the Note7.. and am waiting on the Marlin. But I am not a fan of the edge screen. I like to use a screen protector and case (and use a magnetic mount in my A/C vent). There are times when my phone gets knocked off the magnetic mount, so the screen protector is a must. From what I've seen thus far, screen protectors don't work very well with the edge displays and cases like the Speck CandyShell Grip or the Spigen cases.
Since I tend to buy and use a phone for several years, I'd like to stay with a flagship. I'd also like timely OS and security updates. My 3+ year old GS4 gets none of the above. OTOH, my wife's iPhone 5 (also 3+ years old) gets both OS and security updates. The only way I know to come close to that is go with Nexus and that is only good for 2 and 3 years for OS and security updates.
I don't have overheating issues in the summer with the phone on the magnetic mount in the AC vent. But cooler times of the year could be problematic if a phone tends to run hot.
My camera on the GS4 is so slow to open that I often miss spontaneous shots I like to take. The stock camera app often crashes when I rotate from portrait to landscape orientation. I want a fast and good, low-light camera! If Marlin doesn't impress me, I am considering looking at the iPhone 7. That thought causes a certain amount of angst because I have never been impressed by iOS. And yet I recognize why Apple keeps that walled garden locked down. I wish Android wasn't so fragmented and that the N7 would come out in a GPE edition (and with a flat screen to boot!). Dream on.