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It's not just first gear. The RPM that lugging occurs depends on many factors, of which one is what gear you're in. Torque multiplication due to gearing is a huge factor, thus the higher the gear ratio, the easier to lug the engine.
900 RPM in 7th gear going uphill is entirely different than 900 RPM in 2nd gear gong downhill.
Even the model C7 you are driving factors in as there are three different manual transmissions used and all three have different gearing(thus different torque multiplication in each gear). For example, 7th gear in the base Stingray is .42:1 whereas it's .45:1 in the Z06 and .48:1 in the Z51/GS.
Your grandfather maybe "lugged" the engine on his 1960 Studebaker.
In the past, the ignition, valve activation, and intake were mechanically tied to engine RPM. Typically, at less than 500-600 RPM, the engine could not function. Today, its all computer controlled.
I suppose if you wanted to be a total *** you could put a manual transmission into 7th gear, and stall the engine, but mostly, the engine management system can measure load, and adjust the parameters.
My 2016 A8 can cruise effortlessly at 80 MPH at about 1400 RPM in 8th gear. In normal operation you cannot "lug" the engine.
The danger of lugging the engine is burning the intake valves. While the valve timing has some adjustment, it's not infinite, so I would follow the advice of the manual and avoid large throttle applications at low rpm.
If your're driving an auto, you don't need to think about this since the transmission will downshift for you. But in any case the engine produces so little power at low rpm I can't imagine wanting to drive around at low rpm except for cruising.