The smoothness you're observing is not just the lattice interpolation. The main difference to other applications is the design of Photon's color model "Spindle". The outer shell of the Spindle model is geometrically optimized for color smoothness. On the inner shells it has built in stabalizers, overflow protections and color coalescence simulation. You can actually see exactly what it does as the real underlying color model is rendered in the UI.
Note: As of the time of this post some imported LUTs can visually distort the UI rendered point-cloud in the Spindle, even though the underlying data is interpreted correctly.