Lee's influence on the Union's fortunes would depend on which command he would have been given. Winfield Scott wanted him for a top command and so Lee would have likely taken the spot of McClellan commanding what would be the Army of the Potomac. If so he would have been more realistic about strategic conditions and could have taken opportunities missed by McClellan.
The Confederacy would not have, at first, miss Lee's presence. Lee afterall lost his first battle but as the war drags on the loss of Lee as a grand strategist would have severely undermined the Confederacy's ability to off-set the numeric odds against them. Without Lee, Jefferson Davis would have continued his distracted command of the Confederate Armies without the flexibility to be truly surprising to his opponent.
There would also be some other effects. Arlington wouldn't be the national cemetary as it was Lee's land and house that were seized to build it. Lee also would lose his OTL hero status in the South and wouldn't likely win the legacy in the University of Washington and Lee. Lee's heart might also break depending on how his home state of Virginia sees him in a post war Union though a pro union West Virginia analogue, if it still breaks away, may hold him in higher regard.