  We analyze the weak decay of doubly-heavy baryon decays into anti-triplets
$\Lambda_Q$ with light-cone sum rules. To calculate the decay form factors,
both bottom and charmed anti-triplets $\Lambda_b$ and $\Lambda_c$ are described
by the same set of leading twist light-cone distribution functions. With the
obtained form factors, we perform a phenomenology study on the corresponding
semi-leptonic decays. The decay widths are calculated and the branching ratios
given in this work are expected to be tested by future experimental data, which
will help us to understand the underlying dynamics in doubly-heavy baryon
decays.
