You are not very specific about the time and place that Lee decides the fight will go on. First, he worries that the new Union commander, George Meade, will carry on the fight. A native of Pennsylvania, Lee knows that Meade's knowledge of the area would be a factor. Meade will not run away like the previous commander, Joe Hooker.
"Meade will be... cautious." (Lee, Monday, June 29, Chapter 1: The Spy)
Lee recognizes that the fight will go on after his corps commander, Dick Ewell, fails to take several important--and unoccupied--hills on the first day of battle. Ewell had frozen when the decision needed to be made, and Lee knew he must "look into that." When Longstreet's divisions fail to carry The Devil's Den and Little Round Top on the second day, Lee knows the fight must be carried on for a third day. Finally, after Pickett's Charge fails on the third day and the army is shattered, Lee sees that his badly beaten men still want to fight on. Lee's men beg him to attack again, and when the expected Union counterattack never materializes, Lee knows that his army will live to fight another day. His men are still full of fight, and though the Army of Northern Virginia may be beaten for the first time,
"We shall rest and try it again another day." (Lee, Friday, July 3, Chapter 5: Longstreet)