  We extend parts of the Lagrangian spectral invariants package recently
developed by Leclercq and Zapolsky to the theory of Lagrangian cobordism
developed by Biran and Cornea. This yields a nondegenerate Lagrangian "spectral
metric" which bounds the Lagrangian "cobordism metric" (recently introduced by
Cornea and Shelukhin) from below. It also yields a new numerical Lagrangian
cobordism invariant as well as new ways of computing certain asymptotic
Lagrangian spectral invariants explicitly.
