  The strength of the electron-phonon coupling parameter and its evolution
throughout a solid's phase diagram often determines phenomena such as
superconductivity, charge- and spin-density waves. Its experimental
determination relies on the ability to distinguish thermally activated phonons
from those emitted by conduction band electrons, which can be achieved in an
elegant way by ultrafast techniques. Separating the electronic from the
out-of-equilibrium lattice subsystems, we probed their re-equilibration by
monitoring the transient lattice temperature through femtosecond X-ray
diffraction in La$_{2-x}$Sr$_x$CuO$_4$ single crystals with $x$=0.1 and 0.21.
The temperature dependence of the electron-phonon coupling is obtained
experimentally and shows similar trends to what is expected from the
\textit{ab-initio} calculated shape of the electronic density-of-states near
the Fermi energy. This study evidences the important role of band effects in
the electron-lattice interaction in solids, in particular in superconductors.
