  We calculate the Casimir-Lifshitz force (CLF) between a metallic sphere and a
graphene-coated SiO$_2$ plane and compare our finding with the experiment and
theory by M. Liu \emph{et al.}, PRL {\bf 126}, 206802 (2021), where a non-local
and lossless model for the graphene conductivity (GC) has been used and shown
to be compatible with the experimental results. Recently, that conductivity
model has been shown to be not correctly regularized [arXiv:2403.02279], to
predict nonphysical results in the non-local regime, and being correct only in
its local limit, where its expression is identical to the local Kubo
conductivity model (once also losses are introduced). To compare the
experimental results with the correctly regularized Kubo theory and to clarify
the effective role played by the graphene non-locality and losses in that
experiment, we calculated the CLF using three different models for the GC: the
correct general non-local Kubo model, the local Kubo model, and the
non-regularized and lossless model used by M. Liu \emph{et al.}. For the
parameters of the experiment, the predictions for the Casimir-Lifshitz force
using the three models are practically identical, implying that, for the
experiment, both non-local and lossy effects in the GC are negligible. This
explains why the GC model used in M. Liu \emph{et al.} provides results in
agreement with the experiment. We find that the experiment cannot distinguish
between the Drude and Plasma prescriptions. Our findings are relevant for
present and future comparisons with experimental measurement of the
Casimir-Lifshitz force involving graphene structures. Indeed, we show that an
extremely simple local Kubo model, explicitly depending on Dirac mass, chemical
potential, losses and temperature, is largely enough for a totally
comprehensive comparison with typical experimental configurations.
