I can't speak to his thoughts of monuments being dedicated to him, but there is good evidence that he was against memorializing the Confederacy and the war in general. For example, in a letter written August 5th, 1869, he says

I think it wiser, moreover, not to keep open the sores of war but to follow the examples of those nations who endeavored to obliterate the marks of civil strife, to commit to oblivion the feelings engendered.

This was in response to being invited to Gettysburg to commemorate and mark the operations of each army during the battle.

In another letter about a monument, he wrote

As regards the erection of such a monument as is contemplated; my conviction is, that however grateful it would be to the feelings of the South, the attempt in the present condition of the Country, would have the effect of retarding, instead of accelerating its accomplishment; & of continuing, if not adding to, the difficulties under which the Southern people labour. All I think that can now be done, is to aid our noble & generous women in their efforts to protect the graves & mark the last resting places of those who have fallen, & wait for better times.

I don't know enough about Lee to know whether these sentiments were the same throughout the rest of his life (although he died in 1870, so it's unlikely he changed that much since the second letter), but they do show that at least at some point he wanted to put the war behind the country and move on. Hopefully another contributor can give a better picture.