They had met each other. For all I know Lee had mentioned Grant in one of his reports and recommended him for a distinction. However when Lee surrendered to Grant at Appomatox Grant asked Lee if he remembered him from Mexico, Lee said that he didn't. It was not a very close relationship.
Anyway, this is drawing out too much so with those you've given me you may come up with the next question Nick. Here are some more examples:
General Grant was a good friend of Lee's "Old Warhorse" James Longstreet, who was one of the most famous confederate Generals (who also commanded Pickett's charge even though he had repeatedly protested against that attack). Longstreet attended Grant's wedding and after the war Longstreet became a republican and got offices during Grant's presidency.
One of Pickett's brigades during the infamous charge was commanded by Lewis Armistead, who became famous for being one of the few to make it across the stonewall on Cemetery Ridge (with his hat put on the tip of his sword) before being shot down. He was a very close friend (a brotherlike relationship) to union general Winfild Scott Hancock whose Corps was hit by Pickett's charge. Hancock was seriously wounded during that fight.
Speaking of Pickett's charge, George Edward Pickett himself was so close a friend to Abraham Lincoln that he forbade anyone to talk bad of Lincoln in his presence.
Another general to be wounded during Pickett's charge was John Gibbon of North Carolina, who fought for the north while three brothers of him fought in the confederate army.
General George H. Thomas from Virginia also fought for the union. His family never spoke with him again and a portrait of him hanging in the house of his family was turned to face the wall.
There are many more examples for such tragic splits of families and friendships during the civil war.