How can I calculate mix of these 4 colors when I have
(L,a,b)for each such color?
How can I calculate same mix, if I want to put weights
(w1, w2, w3, w4)on such 4 colors, having 1 maximum and 0 minimum (none) weight?
You should first convert the colors in CIE XYZ, which is a linear space.
How do you want to mix them?
You just multiply each color XYZ's by their weight and sum; this will give you the XYZ coordinate of the resulting color. Then you can convert back your XYZ to Lab.
Could you mix them in RGB and then convert?