Disagree a bit......he indeed gave alot of latitude in how orders were carried out.....it remains the order for Longstreet was to make the attack.........not carrying out the order isn't really latitude in how to carry it out at all.....but a refusal to carry it out.......Lee ran a loose "mission command" type of command structure, and he was of the opinion that corps commanders etc. should be allowed to fight their own battles.
On 3rd July 1863, AP Hill was down sick, leaving Lee with only two principle lieutenants; Ewell commanding his left and Longstreet his right and centre. His instructions to both were for a major converging attack against Cemetery Hill. He indicated that the artillery should make a 15 minute "whirlwind bombardment" and then the infantry should attack.
Longstreet, worried about Federal cavalry off his right flank, detached two whole divisions of the attack force to protect his flank. He was left with 18 brigades to attack with. He effectively ended up with two waves each of 9 brigades, but the second wave was recalled and some brigades never even launched.
Longstreet prevaricated over launching the first wave, and kept the artillery firing for 2 hours until they basically ran out of ammunition and couldn't support the attack. He then launched the 1st wave, but recalled the 2nd wave when the 1st wave failed.
Lee may have been disappointed, but he had given Longstreet a lot of latitude to act as he wished. Perhaps too much.
His letting his troops rest and not being in place earlier.....was that latitude....the attack was still expected however