  We investigate the magnetic properties of the multiferroic quantum-spin
system LiCu$_2$O$_2$ by electron spin resonance (ESR) measurements at $X$- and
$Q$-band frequencies in a wide temperature range $(T_{\rm N1} \leq T \leq
300$\,K). The observed anisotropies of the $g$ tensor and the ESR linewidth in
untwinned single crystals result from the crystal-electric field and from local
exchange geometries acting on the magnetic Cu$^{2+}$ ions in the zigzag-ladder
like structure of LiCu$_2$O$_2$. Supported by a microscopic analysis of the
exchange paths involved, we show that both the symmetric anisotropic exchange
interaction and the antisymmetric Dzyaloshinskii-Moriya interaction provide the
dominant spin-spin relaxation channels in this material.
