So, the lens is the first signal filter in the data stream. In this case the signals are the frequency and amplitude of the light entering the lens. Obviously this assumes a lens filter is not present. Different lens coating formulations filter the signals differently. The sensor photo diode sites (pixels) can't record signal frequencies filtered by the lens coatings. Lenses often have a significant impact on color rendition.
For JPEG users the in-camera raw to JPEG rendition can significantly affect color rendition. Auto WB may or may not be optimal. Unfortunately the JPEG compression destroys much of the information needed to manipulate color temperature during post-porciessing. However in-camer JPEG presents do offer some flexibility to alter color rendition to one's taste.
Raw users usually start the post-processing rendering using the camera's WB parameters. All the data is present in the raw file, so there is no limitation on adjusting the global color temperature. In other words the camera's WB setting doesn't matter. The lens coatings do matter to some degree because the light was filtered before it reached the sensor. Even the raw file does not have all the information (signal content) that entered the lens.
Still, post-processing can cancel the affect of lens coatings. In Photoshop (and other products) one can create a global layer that cancels the lens filtering. It may be tedious to create a layer that replicates a certain lens' color temperature bias, but once you do it the process can be automated. This is no different than adding physical color filters to color print enlargers. In both cases you are adding the signal information removed by the lens coating.
Discussions of color rendition differences between different brands, different models within the same brand and different brands with different lenses are difficult because so many factors affect the final result.
