I was told by a LH attendant that they do not care about carry on dimensions and weight if you are flying Business. Last year I flew ORD-NCE on LH Business and I had no problems with US-sized carry on, but this year LH has gotten strict on Economy passengers so I ended up having to check in my American-sized carry on luggage even before it was weighed. This was at ORD and as I checked in on-line before the flight and had no other checked bags, the carry on was taken at the gate.

Once in Europe, I had short connections in MUC, ZUR and VIE so I didn't want to chance them taking it at the gate and potentially making me late for my flight.

I second a back up plan.