  In our previous work, the connected and leading disconnected hadronic
light-by-light contributions to the muon anomalous magnetic moment (g - 2) have
been computed using lattice QCD ensembles corresponding to physical pion mass
generated by the RBC/UKQCD collaboration. However, the calculation is expected
to suffer from a significant finite volume error that scales like $1/L^2$ where
$L$ is the spatial size of the lattice. In this paper, we demonstrate that this
problem is cured by treating the muon and photons in infinite volume, continuum
QED, resulting in a weighting function that is pre-computed and saved with
affordable cost and sufficient accuracy. We present numerical results for the
case when the quark loop is replaced by a muon loop, finding the expected
exponential approach to the infinite volume limit and consistency with the
known analytic result. We have implemented an improved weighting function which
reduces both discretization and finite volume effects arising from the hadronic
part of the amplitude.
