  We study the Byzantine lattice agreement (BLA) problem in asynchronous
distributed message passing systems. In the BLA problem, each process proposes
a value from a join semi-lattice and needs to output a value also in the
lattice such that all output values of correct processes lie on a chain despite
the presence of Byzantine processes. We present an algorithm for this problem
with round complexity of $O(\log f)$ which tolerates $f < \frac{n}{5}$
Byzantine failures in the asynchronous setting without digital signatures,
where $n$ is the number of processes. We also show how this algorithm can be
modified to work in the authenticated setting (i.e., with digital signatures)
to tolerate $f < \frac{n}{3}$ Byzantine failures.
