Grahame - there is no easy answer for optimizing a mixed light shot. In some cases we can get workable results and in other cases not so much:
1. If we have a good light source on the subject and one that is not as flattering, then we can often just get away with colour correcting the subject and leaving the rest of the image the way it is. This is what is happening with some of Mike's postings, both in this thread and more so in some of the others. Correct the main subject and let the background look a bit funky.
2. If the mixed light sources hit the subject in a defined manner, we can sometimes do what Ted has suggested, colour correct as best we can to the two light sources and then try to blend the two images together. If we are dealing with a human subject, as long as the face looks reasonably good, this might work, but it takes a lot of effort.
Let me demonstrate with an urban landscape where I ran into this issue and tried a number of different approachs.
Image 1 - if I get the left side of the image looking correct, the right side has a very noticeable blue colour cast
Image 2 - if I get the right side of the image looking correct, the left side has a very warm colour cast.
Image 3 - if I stack both images in Photoshop and then blend using a gradient to get the bulk of the work done and then hand-tune the masks, I get something in the middle.
3. Sometimes just leave the colours look off. Theatrical lighting or shooting at a concert, this might be the only practical option. The lights tend to be so heavily gelled that there are some predominant wavelengths that cannot be neutralized.