  We study framed surfaces, which are a class of Euclidean minimal and
hyperbolic CMC-1 surfaces that generalize immersed minimal surfaces in
$\mathbb{R}^3$ and Bryant surfaces. For this class we prove a lower bound on
the (unrestricted) Morse index by a linear function of the genus, number of
ends and number of branch points (counting multiplicity), generalizing a result
by Chodosh and the first author. We include as well a description of the 1-to-1
correspondence between Euclidean minimal and Bryant surfaces, known in the
literature as Lawson's correspondence.
