  The periodic Anderson model (PAM) captures the essential physics of heavy
fermion materials. Yet even for the paramagnetic metallic phase, a practicable
many-body theory that can simultaneously handle all energy scales while
respecting the dictates of Fermi liquid theory at low energies, and all
interaction strengths from the strongly correlated Kondo lattice through to
weak coupling, has remained quite elusive. Aspects of this problem are
considered in the present paper where a non-perturbative local moment approach
(LMA) to single-particle dynamics of the asymmetric PAM is developed within the
general framework of dynamical mean-field theory. All interaction strengths and
energy scales are encompassed, although our natural focus is the Kondo lattice
regime of essentially localized $f$-spins but general conduction band filling,
characterised by an exponentially small lattice coherence scale $\omega_{L}$.
Particular emphasis is given to the resultant universal scaling behaviour of
dynamics in the Kondo lattice regime as an entire function of $\omega^{\prime}
=\omega/\omega_{L}$, including its dependence on conduction band filling,
$f$-level asymmetry and lattice type.A rich description arises, encompassing
both coherent Fermi liquid behaviour at low-$\omega^{\prime}$ and the crossover
to effective single-impurity scaling physics at higher energies -- but still in
the $\omega/\omega_{L}$-scaling regime, and as such incompatible with the
presence of two-scale `exhaustion' physics, which is likewise discussed.
