Lex Luthor (Jesse Eisenberg) is a master manipulator in Batman v Superman: Dawn of Justice, pulling all sorts of strings to coordinate the titular fight between Batman (Ben Affleck) and Superman (Henry Cavill), and he had Batman completely under his thumb the whole time. After seeing Superman damage Metropolis during Zod's attack, Bruce Wayne went down a dark path, bent on destroying Superman, but little did he know he was merely doing Lex Luthor's bidding all along.
Batman certainly had enough motivation to go after Superman, despite the urges of Alfred to back off, but the World's Greatest Detective was so blinded by rage he didn't realize he wasn't uncovering a trail of clues, but breadcrumbs planted by Lex Luthor, who let him track K.G. Beast to his mansion, gave him the space he needed during a party to hack into his network to get his files on metahumans and Kryptonite, let him find the location of the Kryptonite shipment, and finally let him track the shipment back to LexCorp where he broke in and stole it for his own purposes.
While Batman did all the legwork, taking a step back, it becomes clear Lex Luthor was pulling the Caped Crusader's strings the whole time, and even the Kryptonite spear designs appear to have come from Lex himself. As noted on the recent Batman v Superman: By the Minute podcast covering Bruce's workout montage where it shows him preparing to fight Superman, Bruce opens Lex's files about the Kryptonite, which are clearly a part of the same interface colors and graphics of Lex Luthor's storage drive interface. The montage then follows as Bruce carves the spearhead and assembles the spear, suggesting the actual Kryptonite spear designs were also provided by Lex.
Bruce being manipulated in this way by Lex in Batman v Superman has been criticized by some since Batman is supposed to be the World's Greatest Detective, but the idea has plenty of basis in the comics, such as when Dr. Hurt had Batman entirely wrapped up in his schemes in Grant Morrison's Batman R.I.P., or even Batman himself in Mark Wair's JLA: Tower of Babel the bodies of Thomas and Martha Wayne are stolen to distract Batman as the rest of the League is attacked using Batman's own contingencies. Batman's susceptibility to emotional manipulation is probably one of his greatest weaknesses, particularly when it involves his family (genetic, adopted, or otherwise).
In Batman v Superman: Dawn of Justice, Lex knew exactly how to get what he wanted out of Batman, and outright says as much to Superman as he gloats about his master plan "Ripe fruit, his hate. Two years growing. But it did not take much to push him over actually. Little red notes, big bang, you let your family die! And now, you will fly to him, and you will battle him, to the death." While some aspect of Lex's manipulation were more obvious, the fact that he also provided Bruce the instructions for the Kryptonite spear, which Bruce followed to perfection, is probably one of the more subtle aspects of Lex's plan.
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