Here is a [random, scattered, incomplete] list of extensions to Lucas's theory that I am interested in :
 relativistic correction factor is not correct, get rid of (1  beta^2) terms (Ed Dowdye Jr?)
 time lags and causality, Oleg Jefimenko
 fractional order calculus  ?Johan Suyken's student, now prof?

Comparisons to :
 Randall Mills