Sounds like you're going to need a digital surface model -- the higher the resolution the better. If you have LiDAR filter it for first return points, then create create the DSM using the LAS dataset to raster. Once you have a DSM, you might try the area solar radiation tool. This outputs a raster with cells in watts/sq m. so the lower values will be shady, higher values sunny. You can adjust the settings to model a certain time of day if you wanted. Then use the set null tool to set portions of the raster to null where the watts/sq m value is high (i.e. sunny). After that you could buffer the road segment you are interested in and clip the raster to the buffer.
Another alternative would be to use the hillshade tool, adjusting the settings for an appropriate sun azimuth and altitude. You'd again have to decide some threshold in the output raster where values below the threshold are considered shadows. Good luck!