There is an element of truth to the professor's statement, but of course it is an over-broad generality. Always outnumbered, Lee had to be able to hold a good part of the Union army in place while he concentrated a "locally superior" force which was mobile and could hit the enemy hard on the flank. Lee would rely upon entrenchemnts when he could to hold the attention of the major portion of the Union army in check in order to create a large mobile force - an application of the "economy of force" principle as found in today's military teachings.
There are plenty of such examples in Lee's battles, such as Lee's first victory outside Richmond in the first of the Seven Days battles, and of course Chancellorsville, where Lee divided his force three times in order to protect his back from the Union advance from Fredericksburg, another portion to hold Hooker's army in place in the Wilderness, and then sending Jackson off on his famous "left hook" which left Siegel's forces reeling in panic and threatened to collapse the entire Union line.
Of course, this wasn't particularly original military thinking. When attacking the enemy, you have three choices - go around them to the left, go around them to the right, or try to go right through them. The hard part is in the application - at no point can you rely upon the enemy to do what you hope them to do, and any mistakes they make might be remedied quicker than you can take advantage of them. Even Bragg was able to give Rosecran's army at Stones River a good spanking by attacking the Union left flank and rolling it up.
An example of the "mistakes" Lee might have taken advantage of include Chancellorsville (Hooker's left flank was "in the air"), or along the N. Anna line during Grant's Overland Campaign. But this wasn't pure luck - Lee had examined the Union's choices carefully, like a chess player looking at the board from both sides, and already knew well what choices the Union commander would have to make and which of those choices made at least a portion of his army vulnerable. At Chancellorsville Lee knew which routes Hooker would have to take to ford the Rapidan, and sent Stuart's cavalry to watch closely for where Hooker's flanks were anchored. When they reported back that Hooker's left flank was in the air, he immediatly moved to take advantage of it before Hooker could correct the problem. In a sense, he made his own luck.
At the N. Anna, however, the opportunity was a fleeting one caused by the geographics of the river forks which left one portion of Grant's forces isolated. Lee had already anticipated the problem , and when he saw it develope he tried to take advantage of the situation. But Lee was in poor health and unable to supervise the action himself, and Longstreet was still recovering from his wounds. Less capable junior officers were left to conduct the movement, and they encountered vigerous opposition from Union cavalry using repeating rifles. Before the Confederates could correct their problems, Grant saw through Lee's plans and removed the exposed portions of his army to beyond Lee's reach.
On the defensive, such as at Fredericksburg and Anteitam, that's another matter altogether - Lee shuffled forces as needed between threatened positions to avoid being overcome at any given point.