Does a Rotary engine lug?
 

Not that I would really try it, but I have noticed that the engine is incredibly smooth when taking off in first.. no usual bog like most piston engines. Most likely because it doesn't have the reciprocating mass that a piston engine does..

I've found that it does pretty well. For example, you can easily drive around a parking lot in 2nd gear. My buddy cannot do that in his wrx without riding the clutch.

It does very well not to lug easily.

Yeah the engine does pretty well. For instance you can take fairly steep inclines in 5th gear no problem and as mentioned, ride around a parking lot in 2nd gear.

Sure any car can be lugged. Just drive around in 3rd or 4th below 30 MPH.

Any engine can lug if you are in the wrong gear.