Lab is just challenging because I don't know how to generate Lab values for tints. For instance, you need to decide what Lab value for 0% tint (white), 100% tint (full colour), 50% tint (half colour - but what is that?), 20%, 31% etc. Your function takes 0.0 1.0, 0.5, 0.2, 0.31 etc for these percentages and must return the colour components. So for your case 0.0 would return white, 1.0 would return 50.0 -128.0 -128.0 and the others are up to you to decide. This is something you need the answer to before you can start. For most colour spaces the first attempt (but necessarily the best) is likely to be linear. For example if 100% tint is RGB 0 0.8 0.2 then 50% tint is 0 0.4 0.2. CMYK is more complicated as reducing the values goes closer to black, rather than closer to white.
For non-Lab colour spaces the issue are the same. I am not going to write PostScript functions for you . There is an example of a 2-in 1-out function in the spec. Despite 20 years experience of PostScript, I find this a fiddly and annoying task because of the stack architecture. .
I don't know why you picked a type 4 function if you don't know PostScript. Perhaps it seemed simpler? I recommend you use the basic function type 0 instead. You can precalculate your tint values at different points on the 3x3 grid, and fill in this as a table.