it really depends on how lean you go, and how hard you ride the bike in it's lean condition. when lean, your bike will run hotter than usual. if it gets too hot, you burn up the heads. i'm oversimplifying it but that's the general risk.
The damage is not likely to be immediate. It would depend on outside temp, and how long and hard you rode with the lean condition. The injected bikes would compensate some automatically, but not enough to just let it go.
A 4 stroke is much more forgiving than a 2 stroke, but yes, you can definatly still burn a motor down. Early signs will be burned spark plug insulators & little bits of aluminum (from the piston tops) adhered to the spark plug electrode. If you can gain enough access to see the top of the piston, it will have a melted surface look to it. Eventually, the top of the piston melts thru & makes a hole. The good news is that this usually doesn't take out the bottom end unless the piston seizes. All of this rarely happens unless you run the motor at sustained high RPMs, like in a racing environment.
weber marelli injection as employed by ducati is open
circuit N / alpha .... no
feedback (apart from a water temperature input
which serves as the idle 'enrichener') from an
exhaust oxygen sensor to detect a lean condition.
the color of the exhaust soot is a 0-th order method
of checking mixture.
if the soot on the inside of the exhaust outlet is
white .... that's a good indication that the bike is
running lean (black indicates rich, tan = just right).
too rich isn't good either since excess fuel will tend to
get past the rings and dilute the oil film between the
cylinder and rings.
Well checked the sparkplugs. One is tanned kind of like instant coffee in a jar, the other greayish. Not very light, but not brown like the other. Should be ok I guess. The electrode surface is very even and tidy. The cermic insulation is white (champion plugs) and no discolouration.
Still running into problems with performance, although i closed the lid of the air filter (less air - make the mix richer). I was inspecting fuel line and found out that there is something which i in the workshop maual is called breather hose and drain hose whic come together to one hose and run all the way down below the bike. Now this hose was totally bend, when the tank closes. Perhaps the reason why the bike stumbles and will not run more than 120 km/h at full throttle ??
Lean is one thing, not going over 120 km/h is a problem. I weigh a hair over 260 lbs, i have an open airbox, (which leans the mixture) and i get my bike up to 80 or 90 mph in a heart beat, with a sh*tload of power still left. You have a blockage or worse. Look more closely.
Sorry for being such a dork, but what is a DP kit? I think you have a fuel delivery issue somewhere along the way, or even more basic could be a bad plug. I would probably change the plugs first, if it persists the lines and cylinder heads should be thoroughly checked, but you are losing power not from too much air but not enough fuel. The popping is an indicator of that. I am not sure where you are located, but if you are in the new york area I will strongly suggest formula 1 in bayshore or queens, or cycleconnection in north jersey. However it may be, I am pretty confident without speaking for most others with an open airbox, that this is not an airbox situation.
Good luck, I would be curious to know what it turns out to be in the end. I have to tell you, I feel real bad that you are going through this on a new bike but at least you have the warranty behind you. good luck.