The present paper is a continuation of a previous one [Ann. Global Anal. Geom. 19, No.~4, 355-376 (2001; Zbl 0989.53030)], and generalizes the results to the submanifold Dirac operator. In particular, they obtain optimal lower bounds of this operator in terms of the mean curvature and geometric invariants, e.g. Yamabe number and the energy-momentum tensor. It is also shown that in the limiting case the submanifold is Einstein if the normal bundle is flat. Contents include: an introduction; the submanifold Dirac operator; lower bounds for the eigenvalues; conformal lower bounds; generalized conformal lower bounds; and the energy-momentum tensor. The paper concludes with a bibliography of nineteen items.