Lee did not care about the larger strategic vision of the war. He only cared about the defense of his native state, Virginia, and his actions are very suggestive of this. He was notorious for refusing to lend out brigades or for attention towards other theaters.
I don't understand where you get the impression that the Union generals were attacking on behest of their government. Both of Grant's predecessors, McClellan and Halleck, as commanders of the army, were sacked for their reluctance to take the war to the enemy.
Lee did not have "hundreds of thousands of men." His army, the Army of North Virginia had a rough figure of around 70,000 men, give or take a few thousand. It's also been documented many times over that his men were pretty good at living off the land.
The North did not bother converting the rail system of the South, they spend their time tearing it up (Sherman, et al).
The only importance that LRT contributed to the battle of Gettysburg was the Union being able to hold off the South there. It would have ended in a stalemate if Lee hadn't forced his hand by throwing Pickett's division at them.