Several mechanisms to produce lithium-rich red giants have been proposed, including interactions between the red giant and a binary companions as the star reaches the tip of the red giant branch. One consequence of this model would be tidal spin-up of the red giant to the few km/s level. This level of rotation could in principle be detected in photometry from missions like Kepler and TESS, but signals longer than ~50 days are typically overwhelmed by instrumental systematics and removed by the processing pipeline. Here, we describe our data-driven reanalysis of Kepler pixel-level data that more accurately preserves slower signals in the data and our measurements of rotation periods of the lithium-rich giants in the Kepler field compared to lithium-normal giants and the implications for the formation of lithium-rich giants, as well as the potential to apply this method to other cool stars with 100-day or longer rotation periods.