Haku couldn't even blitz a Sasuke who just reawoke his Sharingan. That same Sasuke got blitzed by a Lee with weights on. Therefore Haku has no hope of blitzing someone who consistently beat weightless Lee, and who Lee learnt the Extreme Lotus in order to defeat. Neji counters Haku's needles with Rotation, then takes him out with a Jyuken palm strike to the heart. Or he simply forces Haku to engage in close combat before the Mirrors come up due to the short starting distance.