  We establish the pluri-Lagrangian structure for families of B\"acklund
transformations of relativistic Toda-type systems. The key idea is a novel
embedding of these discrete-time (one-dimensional) systems into certain
two-dimensional pluri-Lagrangian lattice systems. This embedding allows us to
identify the corner equations (which are the main building blocks of the
multi-time Euler-Lagrange equations) with local superposition formulae for
B\"acklund transformations. These superposition formulae, in turn, are key
ingredients necessary to understand and to prove commutativity of the
multi-valued B\"acklund transformations. Furthermore, we discover a
two-dimensional generalization of the spectrality property known for families
of B\"acklund transformations. This result produces a family of local
conservations laws for two-dimensional pluri-Lagrangian lattice systems, with
densities being derivatives of the discrete 2-form with respect to the
B\"acklund (spectral) parameter. Thus, a relation of the pluri-Lagrangian
structure with more traditional integrability notions is established.
