  As a joint explanation for the dark matter (DM) problem and the muon $(g-2)$
anomaly, we propose a simplified model of lepton-flavoured complex scalar DM
with couplings to both the left- and right-handed leptons of the Standard Model
(SM). Both interactions are governed by the same new flavour-violating coupling
matrix $\lambda$, however we allow for a relative scaling of the coupling
strength. The SM is further extended by two fermion representations,
transforming as an $SU(2)_L$ doublet and singlet, respectively, and mediating
these interactions. The fermions additionally couple to the SM Higgs doublet
via a new Yukawa coupling. To study the model's phenomenology we first
investigate constraints from collider searches, flavour experiments, precision
tests of the SM, the DM relic density, and direct as well as indirect detection
experiments individually. We then perform a combined analysis by demanding that
all mentioned constraints are satisfied simultaneously. We use the results of
this combined analysis and examine if the model is capable of accommodating the
$(g-2)_\mu$ anomaly within its viable parameter space without introducing
fine-tuned lepton masses. For all benchmark scenarios we consider, we find that
the central value of $\Delta a_\mu^\text{exp}$ can be reached without
generating too large corrections to the lepton masses. We hence conclude that
this model qualifies as a viable and attractive lepton-flavoured DM model that
at the same time solves the $(g-2)_\mu$ anomaly.
