That said, FSD seems quite capable of routing around standing water in many cases (e.g. https://xcancel.com/planoken/status/2030754820462633031, https://www.reddit.com/r/TeslaFSD/comments/1pw9f2m/fsd_navig..., https://xcancel.com/BLKMDL3/status/1991862465328779317, https://xcancel.com/JVTacoma/status/2046313902749921638), so handling the remaining cases seems more like a model intelligence / data issue rather than a sensor limitation. Lidar beams generally bounce off mirrorlike surfaces without returning to the sensor, so I think all lidar would tell you about standing water is "there's something shiny/reflective within this region of the image", which you already know from cameras+headlights.
https://abc7news.com/post/san-francisco-leaders-press-waymo-...