Good. One score. Of course, it is a tetration definition, nice that it works also for I/x , but values for Lambert function of such arguments like are not so obvious (were not initially).
W(-x*(pi/2) - I*x*ln(x) ) = ln(x) - I*(pi/2)=ln(x)-lnI=ln(x/I) for x>1
W(-x*(pi/2) - I*x*ln(x) ) = ln(x) - I*(pi/2)=ln(x)-lnI=ln(x/I) for x>1

