  We propose a universal ensemble for random selection of rate-distortion
codes, which is asymptotically optimal in a sample-wise sense. According to
this ensemble, each reproduction vector, $\hbx$, is selected independently at
random under the probability distribution that is proportional to
$2^{-LZ(\hbx)}$, where $LZ(\hbx)$ is the code-length of $\hbx$ pertaining to
the 1978 version of the Lempel-Ziv (LZ) algorithm. We show that, with high
probability, the resulting codebook gives rise to an asymptotically optimal
variable-rate lossy compression scheme under an arbitrary distortion measure,
in the sense that a matching converse theorem also holds. According to the
converse theorem, even if the decoder knew $\ell$-th order type of source
vector in advance ($\ell$ being a large but fixed positive integer), the
performance of the above-mentioned code could not have been improved
essentially, for the vast majority of codewords that represent all source
vectors in the same type. Finally, we provide a discussion of our results,
which includes, among other things, a comparison to a coding scheme that
selects the reproduction vector with the shortest LZ code length among all
vectors that are within the allowed distortion from the source vector.
