During the Overland Campaign, Lee pretty much nailed what Grant was going to do every time, with the single and disastrous exception of Grant's movement to the south side of the James River.
Sorry but no.
May 7-8: Lee has no idea Grant plans to move the whole army south out of the Wilderness. He does believe something of a southward oblique shift may happen, so he orders Anderson (commanding 1st corps) to move his men southward a bit to counter. Anderson gets confused about the orders, and doesn't see a good place to bivouac for the night, so he keeps his men marching far beyond what Lee intended, and by accident they near Spotsylvania Court House just in time to help out Stuart against Sheridan. Lee gets the inside line at Spotsylvania by pure luck.
May 10: Upton's attack on Ewell is a complete surprise. Lee is currently to the west of the Po River planning an attack against Hancock's exposed corps, planning to use 2-3 divisions in a pincer movement. Without his guidance Upton's attack succeeds and breaks open the Confederate line for over an hour, but it goes unexploited.
May 11-12: Lee thinks Grant will move around his right again, so he removes all of the artillery from the Mule Shoe salient. Without this force backing Ewell's corps, the attack of the 2nd and 6th corps completely shatter Ewell's men and Spotsylvania comes within a hairsbreadth of Confederate disaster.
May 14: Grant tries to locally outflank Lee at Spotsylvania, and moves the 5th and 6th corps to attack Lee's right flank. It doesn't work because the night march involved turns into a huge tangle, but Lee doesn't shift right to counter for a full 2 days.
May 18: Now Grant tries to outflank Lee locally on the left, by sending the 2nd and 6th corps back over the Bloody Angle and assault Lee's new line. This time the artillery is in place and Ewell smashes the attack, but the actual assault is a complete surprise - Lee thinks Grant will move south again.
May 20-21: Lee thinks Grant will outflank him via Telegraph Road, so he sends Ewell's corps to Stannard's Mill at the Matta (?) River, an ideal blocking position. Instead, Grant sends Hancock far down the Mattaponi River, and he gets over 10 miles beyond Ewell's flank and in an ideal position to crush his corps with Warren's help from the north. It fails because of arriving Confederate reinforcements (Pickett's men) being in the right place by sheer luck, and Hancock being a bit more cautious than usual.
May 23-24: Lee thinks Grant is far behind him in the race to the North Anna River, so he gives his army a day of rest. Instead, Hancock crosses the river at Telegraph Road and Warren crosses at Jerico Mills, and skirmishes at both locations fail to dislodge them. Lee makes it work with his inverted V defense at Ox Ford.
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I forget the details for the Cold Harbor phase of operations, but I think Lee makes another one or two comparable lapses of judgement.
Lee's strength in the Overland Campaign (as first judged by Gordon C. Rhea, and I support this view) had
nothing to do with predicting what Grant would do - because he completely failed at this.
Lee's strength was making the best of bad situations, which he did with amazing regularity. He made several mistakes, but he fixed them quickly, and Grant failed to exploit them because he was getting used to working with the Army of the Potomac. And on more than one occasion Grant chose not to attack the Confederates because he was sure Lee would have set up entrenchments to block such an assault, as Lee surely should have, when in fact Lee had no idea Grant was even contemplating such an attack and his line there was weak or non-existent. The Overland Campaign was a game of bluff and counter-bluff.