Lee mis-read Grant's plans during the Overland Campaign *frequently*, with May 11-12 at Spotsylvania being only the most famous (such as it is). To further @Arnold d.c.'s point:
While Lee surmised that Grant was planning to move out of the Wilderness on May 7-8, he was not sure of this (thinking a withdrawal towards Fredericksburg was also possible), and he never imagined Grant would move as far south as Spotsylvania, thinking Todd's Tavern was more likely. He ordered Anderson to move Longstreet's Corps to block this position, and only a lack of places to set up camp and bad maps kept Anderson marching through the night to arrive at Spotsylvania just minutes ahead of Warren and the V corps.
As Arnold may have said (I'm unsure which 2 occasions specifically he's thinking of), Lee failed to predict Grant would try to flank him out of Spotsylvania on May 14-15, and ultimately the V and VI corps were sitting on the Confederate right flank opposing 1 division, and failed to attack only because they were exhausted from the night march, and by the time they recovered Grant wrongly assumed that Lee would have reinforced this flank.
Then on May 18 Lee failed to predict that Grant would move the VI corps back towards the Confederate left flank, and repeat the May 12 assault but jumping off from the Mule Shoe line (now Union-controlled) against the new line at its base. Confederate artillery (in place this time) blasted the assault apart, but the attack itself was a complete surprise.
Lee utterly misread Grant's wide flanking move on May 20-21, and as a result had the II and V corps dozens of miles southeast of the Confederate position (now with Ewell emplaced at Stannard's Mill), and this failed to be a disaster only due to newly arriving Confederate forces under Breckenridge and Pickett, and again the Union's false supposition that Lee would surely be defending his right flank.
And then again on May 23, Lee thought that Grant would not possibly be pursuing so closely, and failed to fortify the line at the North Anna River. This resulted in a Confederate brigade surrendering (at Henegan's Redoubt) and the Light Division wrecking itself attacking the vastly more numerous V corps trying to force it back into the River. Lee's defense along the river was broken before it was even tested, and only him finding the inverted-'V' position saved his army.
Then on May 26-27 Lee was yet again fooled when Grant moved away from the River, marching some tens of miles downriver before recrossing. Lee was able to find the Totopotomoy Creek defensive line due to having a shorter distance to march, but it could have been a tie or a Union win in the race if they had moved with any dispatch after crossing the Pamunkey.
There was at least one more comparable lapse in Lee reading Grant in the Cold Harbor phase of operations, which I forget the details of at the moment (and don't want to look up Rhea's books to re-find). Arnold has already mention the surprise of the move to the James.
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Lee's strength in the Overland Campaign was in being able to make the best of a bad situation, and turn pretty much any line into an impregnable defense against frontal assault (missing artillery at Spotsylvania the exception that proves the rule); it was also in being able to bluff and counterbluff Grant's moves with strategic counterpunches, cavalry raids, and utilizing backroads and the terrain to its fullest extent. It was emphatically *not* predicting what Grant would do, because he utterly *failed* at this.
Good points (from Arnold DC) and I recall something about Cold Harbor as well (although the specifics escape me at the moment). I noted the surprise at the James River as well... if only Baldy Smith had pushed in those few hours at Petersburg! Although most likely Lee would still have found a way to keep disaster at bay a bit longer. Mule Shoe was one of those might have been's, indeed for a brief moment (until Lee managed to rally them), his Army was in deep trouble and in danger of route.
The point about Lee missing the Union movements is important here. There is criticism about the Union cavalry not doing its job in scouting for Grant. However the Confederate Cavalry isn't doing its job here either because it is busy trying to hold off said Union Cavalry elsewhere. So both Armies are moving through the second growth woods on the Wilderness without much of the way of scouting available, and thus a series of meeting engagements through the entire campaign.