Hi Todd,
The majority of people seem to opt for surgery, which seems pretty successful, but if that is not an option from a financial perspective, then herbs should be used.
Lipid accumulations signify either Damp or Blood stasis. Given the blood-tinged nature of the chyle in many animals, and the upper burner location, we've tried Xue Fu Zhu Yu Tang with some success. It may need modification, specifically the incorporation of more blood moving anti-lipidemia herbs.
The other thing to bear in mind is that the Triple Burner equates to the pleural and parietal spaces, so we would literally have a Damp or Blood stasis accumulation in the Triple Burner. This would suggest the need for concomitant use of a TB formula. I would immediately think of Xiao Chai Hu Tang for this, and would use it in concert with XFZYT, especially if there were active GB points.
So those are the differentials to watch out for, in the event the case comes to you. Is it possible to deal with it using TCM? Yes. Can you guarantee a consistent outcome? Not yet, because so many people don't use TCM in isolation, but opt for surgery. Definitely we've seen improvements, though before these other measures are taken, so it's worth a try.
Steve