The idea is very simple, and can be found described in many web sites, and also in the manual of Fractint.
Click to enlarge
I used a trick to avoid slow computation time, since the Lyapunov exponent is as
one can use the properties of the logarithm to transform the expression above into
so that the expensive logarithm operation has to be computed only once after the iterations, and not once per iteration. This of course has the problem of precision, since the multiplication of derivatives can quickly get huge.
I experimented with these back in 2001 (see image above), and then remade it in Shadertoy for your referene: https://www.shadertoy.com/view/Mds3R8