  We compute for the first time the decay width of lambda-hypernuclei in a
relativistic mean-field approximation to the Walecka model. Due to the small
mass difference between the lambda-hyperon and its decay products---a nucleon
and a pion---the mesonic component of the decay is strongly Pauli blocked in
the nuclear medium. Thus, the in-medium decay becomes dominated by the
non-mesonic, or two-body, component of the decay. For this mode, the
lambda-hyperon decays into a nucleon and a spacelike nuclear excitation. In
this work we concentrate exclusively on the pion-like modes. By relying on the
analytic structure of the nucleon and pion propagators, we express the
non-mesonic component of the decay in terms of the spin-longitudinal response
function. This response has been constrained from precise quasielastic (p,n)
measurements done at LAMPF. We compute the spin-longitudinal response in a
relativistic random-phase-approximation model that reproduces accurately the
quasielastic data. By doing so, we obtain hypernuclear decay widths that are
considerably smaller---by factors of two or three---relative to existing
nonrelativistic calculations.
