  We consider universal variable-to-fixed length compression of memoryless
sources with a fidelity criterion. We design a dictionary codebook over the
reproduction alphabet which is used to parse the source stream. Once a source
subsequence is within a specified distortion of a dictionary codeword, the
index of the codeword is emitted as the reproduced string. Our proposed
dictionary consists of coverings of type classes in the boundary of transition
from low to high empirical lossy rate. We derive the asymptotics of the
\epsilon-coding rate (up to the third-order term) of our coding scheme for
large enough dictionaries.
