  It is shown that dynamical screening of the Coulomb interaction in LaCuO
leads to low-energy electronic collective excitations in a small region around
the c-axis, strongly mixing with interlayer phonons. The manifestation of such
a phonon-plasmon scenario based on a nonadiabatic charge response is
quantitatively supported by a realistic calculation of the frequency and
wavevector dependent irreducible polarization part of the density response
function. The latter is used within linear response theory to calculate the
coupled mode dispersion in the main symmetry directions of the Brillouin zone
and the charge density redistributions excited by certain strongly coupling
phonon-like and plasmon-like modes. Moreover, the corresponding mode induced
orbital averaged changes of the selfconsistent potential felt by the electrons
are assessed. Our analysis should be representative for the optimally to
overdoped state of the cuprates where experimental evidence of a coherent
three-dimensional Fermi surface and a coherent c-axis charge transport is
given. It is demonstrated that modes from the outside of a small region around
the c-axis can reliably be calculated within the adiabatic limit. Only a minor
nonadiabatic correction is found for these modes in form of stiffening of the
high-frequency oxygen-bond-stretching mode at the X-point which is attributed
to dynamical reduced nesting. On the other hand, modes inside the nonadiabatic
sector of the BZ have to be determined nonadiabatically owing to the poor
dynamical screening of the long-ranged Coulomb interaction around the c-axis by
the slow charge dynamics. In particular, the relevance of the strongly coupling
phonon-like apex oxygen $Z$-point breathing mode at about 40 meV is emphasized
whose mode energy decreases with less doping.
