Reflection and refraction by moving charge: can method of images be used?

Suppose we have a point charge moving inside the halfspace $z>0$ with a given trajectory $r(t)$. Assume that $z>0$ halfspace is Vacuum and the $z<0$ halfspace is glass or some linear dielectric with electric constant $epsilon_1$.

How can we describe the total electric and magnetic fields generated? If the charge is static then the solution is classical and can be found in any textbook, the field in $z>0$ can be described as a superposition of the fields of the original point charge and a reflected "image" charge, while for $z<0$ it is a scalar multiple of the original field.

Is there a similair technique to describe the electric and magnetic fields in the electrodynamic case? E.g., would it involve moving image charges generating Lienard-Wiechert fields? If so, how would the varying speed of lights be explained?