Lee's father was at this battle. Greene had superiority of numbers, but chose to let the British attack, and decimated their forces:
Lee didn't even have superiority of numbers, but chose to attack, with Pickett's Charge, and his army was similarly weakened.
Is there any evidence that Lee would have studied this battle? Hindsight is 20/20, but I can't help but imagine him listening to his father recount the battle as a younger man, and then hear his father's voice in his mind while contemplating Pickett's Charge.
Major General Nathanael Greene, defending the ground at Guilford Courthouse with an army of almost 4,500 American militia and Continentals, was tactically defeated by a smaller British army of about 1,900 veteran regulars and German allies commanded by Lord Charles Cornwallis. After 2 1/2 hours of intense and often brutal fighting, Cornwallis forced his opponent to withdraw from the field. Greene's retreat preserved the strength of his army, but Cornwallis's frail victory was won at the cost of over 25% of his army.
https://www.nps.gov/guco/learn/historyculture/index.htm
The Continentals were similarly trying to wear down British support for an expensive war, and I wonder why didn't seem to take these lessons from his father's experience.
tl;dr: Do we know how much Robert E Lee would have learned from Harry Lee, and specifically how often he implemented tactical strategies from his father's experiences?
It bears mentioning that Harry Lee abandoned his family when Robert E. Lee was nine, so there wasn't really a close personal relationship as a foundation.
Lee was interested in his family's genealogy and military history, but I haven't read anything from him that suggests he specifically emulated his predecessor's operations. From what we can see of his library records, there's a chance he may have red about Greene and Light Horse Harry Lee, as he is known to have checked out the encyclopedia American Biography, but what he gleamed from it is known only unto God. We do know he read the memoirs of Napoleon, as well as those of his General Savay, Duke of Rovigo, and Baron Jomini's Art of War.
Frankly, I think it's a silly paradigm. Finding battles where one side suffered more casualties than the other, whether attacking or defending, is easy to the point of meaninglessness. Choosing the right strategy, coordinating the marches, and fighting the troops to win the battle, campaign, and war is much harder than finding historical examples of one method succeeding or failing.
Furthermore, the revolutionary changes in military practice since the American Revolution, as well as the very different strategic situation faced by the Confederacy rendered its tactical and strategic lessons (whatever they were) essentially obsolete. The emergence of mass citizen armies, their organization into several corps, and the fusion of strategic and tactical maneuver were the great innovations of the Napoleonic Wars, and they put the American Civil War into an altogether different epoch than the American Revolution. At Gettysburg, Lee commanded an army of three corps, each essentially an army unto itself; all of them were at least four times the size of Greene's force. Armies in different ages handle differently, and adhering to outdated tactics is a recipe for disaster.
Within the broader strategic picture, Lee's judgement was sound. By carrying the war into the North, he cleared the Shenandoah Valley of Union presence, gave the economy of northern Virginia a respite, supplied his army off enemy territory, and threatened a Northern state capital during a key gubernatorial election year.
This was secondary to his main purpose, though. Writing to Jefferson Davis, he placed the hopes of victory for the Confederacy on 'the friends of peace' in the north, i.e. the peace wing of the Democratic Party. When it seemed like the U.S. was losing the war, they gained strength. Lee could think of no better way to convince the Northern public that the war was a failure than by pillaging Pennsylvania with impunity, then finding the main Union field army and kicking its teeth in.
In war, all combatants possess an independent will. It'd be nice if you could make the enemy blunder a victory into your hands, attacking uphill one brigade at a time all afternoon December 12, 1862, but that depends on the enemy being saddled with an inexhaustible supply of Ambrose Burnsides. Just because Lee wants to defend a strong position doesn't mean the enemy will play along. They might wait for his supply lines to falter, or might try to cut him off from his line of retreat, or simply wait for him to attack. If they did attack his position, it would only be when they had their entire army in place, and they were ready for it. The only way for him to fight the Union army when it was unready was to attack it, and as soon as possible. There's a reason Offensive: seize, retain, and exploit the initiative is one of the core principles of war; having a purely negative aim, the defensive cannot produce results on its own.