  We report on a heat capacity study of high quality single crystal samples of
\lcvo\ -- a frustrated spin $S=1/2$ chain system -- in magnetic field amounting
to 3/4 of the saturation field. At low fields up to about 7~T, a linear
temperature dependence of the specific heat, $C_p\propto T$, resulting from 1D
magnetic correlations in the spin chains is followed upon cooling by a sharp
lambda anomaly of the transition into a 3D helical phase with $C_p\propto T^3$
behavior at low temperature. The transition from a spin liquid into a
spin-modulated (SM) phase at higher fields occurs via a hump-like anomaly
which, as the temperature decreases further turns into a $C_p\propto T^2$ law
distinctive for a quasi-2D system. We suggest an explanation for how
nonmagnetic defects in the Cu$^{2+}$ chains can suppress 3D long-range ordering
in the SM phase and leave it undisturbed in a helical phase.
