Conversion from srgb to lab and back (through xyz) is a handful of functions, all under a dozen lines of javascript. Lab to lch and back are a pair of functions, about two lines of code each.

If you're implementing a user interface with sliders, you might also want to clamp the values to avoid producing out of gamut colours. The weird shape is probably the hardest thing to understand (user point of view), but the controls remain very intuitive.