  We present a theorem in d-dimensional static, spherically symmetric spacetime
in generic Lovelock gravity coupled with a non-linear electrodynamic source to
generate solutions. The theorem states that irrespective of the order of the
Lovelock gravity and non-linear Maxwell (NLM) Lagrangian, for the pure electric
field case the NLM equations are satisfied by virtue of the Einstein-Lovelock
equations. Applications of the theorem, specifically to the study of black hole
solutions in Chern-Simons (CS) theory is given. Radiating version of the
theorem has been considered, which generalizes the Bonnor-Vaidya (BV) metric to
the Lovelock gravity with a NLM field as a radiating source. We consider also
the radiating power - Maxwell source (i.e. $\(F_{\mu \nu}F^{\mu \nu}\)^{q},$
$q=$ finely - tuned constant) within the context of Lovelock gravity.
