Why is it that we make Shehechiyanu both nights of Sukkos at candle lighting and Kiddush due to Sefeika DeYoma yet we only make Shehechiyanu on the Lulav on the first day?
Because in theory you could have said Shehecheyanu when you prepared (bound) your lulav before Sukkos. So even supposing that the second day of Sukkos was the real Yom Tov (and the previous day was actually erev Sukkos), your Shehecheyanu then would still count as the real thing. (By contrast, with kiddush, you're saying the berachah because of the holiday itself - and conceivably it hadn't yet started the first night.)
(Mishnah Berurah 662:2, citing posekim)