  We describe a new general connection between $\Lambda$-coalescents and
genealogies of continuous-state branching processes. This connection is based
on the construction of an explicit coupling using a particle representation
inspired by the lookdown process of Donnelly and Kurtz. This coupling has the
property that the coalescent comes down from infinity if and only if the
branching process becomes extinct, thereby answering a question of Bertoin and
Le Gall. The coupling also offers new perspective on the speed of coming down
from infinity and allows us to relate power-law behavior for $N^{\Lambda}(t)$
to the classical upper and lower indices arising in the study of pathwise
properties of L\'{e}vy processes.
