The low-dimensional $s=1/2$ compound (NO)[Cu(NO${}_{3}$)${}_{3}$] has recently been suggested to follow the Nersesyan-Tsvelik model of coupled spin chains. Such a system shows unbound spinon excitations and a resonating-valence-bond ground state due to spin frustration. Our Raman scattering study of (NO)[Cu(NO${}_{3}$)${}_{3}$] demonstrates phonon anomalies as well as the suppression of a broad magnetic scattering continuum for temperatures below a characteristic temperature, $T<{T}^{*}\ensuremath{\approx}100$ K. We interpret these effects as evidence for a dynamical interplay of spin and lattice degrees of freedom that might lead to an instability at lower temperatures.