Assuming that LCHF=Low Carb High Fat? From the perspective of a long-term RNY vet and new DS revisionista, here's my $.02:
I had to eat a Low Carb, Low Fat, Low Sugar diet just to maintain the RNY for many years. The thing is, you often end up eating a lot of "fake" food (eg: laughing Cow cheese, Walton Farms sugar free, etc.). It doesn't taste very good, isn't satisfying, and the food is often lacking in nutritional value and can have a high amount of undesirable ingredients. Anyone can eat this way for a while, but let me tell you that it gets old after a decade and it can be worrisome to be so limited during pregnancy or during health challenges. Specific to the RNY, I was limited as to the kinds of protein I could tolerate without throwing up.
The nice thing about being able to eat fat is that we are able to eat whole foods, like meat and cheeses. Fat makes things taste better and is more satisfying (which I believe makes us eat less).