  Analyses of Lunar Laser Ranging data show that the spin-symmetry axis of the
Moon is ahead of its expected Cassini state by an angle of $\phi_p$ = 0.27
arcsec. This indicates the presence of one or more dissipation mechanisms
acting on the lunar rotation. A combination of solid-body tides and viscous
core-mantle coupling have been proposed in previous studies. Here, we
investigate whether viscoelastic deformation within a solid inner core at the
centre of the Moon can also account for a part of the observed phase lead angle
$\phi_p$. We build a rotational dynamic model of the Cassini state of the Moon
that comprises an inner core, a fluid core and a mantle, and where solid
regions are allowed to deform viscoelastically in response to an applied
forcing. We show that the presence of an inner core does not change the global
monthly Q of the Moon and hence, that the contribution from solid-body tides to
$\phi_p$ is largely unaffected by an inner core. However, we also show that
viscoelastic deformation within the inner core, acting to realign its figure
axis with that of the mantle, can contribute significantly to $\phi_p$ through
inner core-mantle gravitational coupling. We show that the contribution to
$\phi_p$ is largest when the inner core viscosity is in the range of $10^{13}$
to $10^{14}$ Pa s, when the inner core radius is large and when the free inner
core nutation frequency approaches a resonance with the precession frequency of
$2\pi/18.6$ yr$^{-1}$.
