For me, it's irrelavent whether is lateral or longitudinal, purple, red, or cyan. It's all junk and needs be ignored or removed. And if removed, with the simplest and quickest method possible.
Removal tools fall into 3 categories:
1. Raw converters, like ACR, provide some CA sliders. My experience is only with ACR, and I think it does a poor job. When it removes the CA in one area it often adds CA in another area. Getting it all out often requires multiple conversions and tedious masking. Maybe other converters like Dx0 do a better job.
2. Third party noise reduction software. Noiseware, Noise Ninja, etc. While these do a good job at removing normal noise, I find they do a poor job removing CA. Farily worthless, in fact.
3. Photoshop PP, which has a few methods.
3A. Targeting the CA "color" and desaturating. Most often this turns a color fringe into a white or gray fringe. Still a fringe. And it requires tedious masking because the desat will impact other areas of the image.
3B. Targeting the CA and using Match Color or Replace Color. Works a little better than desat, but requires very precise masking and multiple steps for multiple colors.
3C. Going to LAB mode and bluring the A channel, or B channel, or both. Usually only the A channel needs blurred. Works amazingly well, but often leaves a little halo. Also requires some masking to protect other areas, but easy and quick masking. Just black mask it and paint over the CA with white.
3D. Finally, the old Photoshop noise reduction tool. I mention this one last, because I think it works best. Filter/Noise/Reduce Noise. Set the Strength and Sharpen Details to 0 and just work the Reduce Color Noise slider. It also creates a halo sometimes. But that halo is far less bothersome than the fringe. The halo can be removed with masking, but that takes some fine control.