It's possible Charles Lee, being the most experienced candidate, actually takes over as Commander-In-Chief. He was a relatively skilled commander with plenty of experience, moreso than even Washington.
That said, he was also a slovenly foul-mouthed eccentric. If he does take command, he may not have the sheer political acumen of Washington - but he'll win far more actual engagements. What this means for the revolution is uncertain.
OTL, Lee created the defenses for Sullivan's Island, which resulted in a major defeat of Henry Clinton's attack on Charlestown. His only other major action was at Monmouth, where he seemed to have been intentionally turning coat much like Benedict Arnold, muddying Washington's strategic plans. It is likely, ITTL, that Lee and Arnold would be the major military commanders without a political schlub like Washington at the helm.
EDIT: He was also a friend of Horatio Gates - so the unfortunate man may still gain a command.