  Extending the approach developed by Ara\'ujo and Stoeger [1] and improved in
Ara\'ujo {\it et al} [2], we have shown how to construct dust-filled $\Lambda
\neq 0$ Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) cosmological models
from FLRW cosmological data on our past light cone. Apart from being of
interest in its own right -- demonstrating how such data fully determines the
models -- it is also illustrated in the flat case how the more general
spherically symmetric (SS) Einstein field equations can be integrated in
observational coordinates with data fit to FLRW forms arrayed on our past light
cone, thus showing how such data determines a FLRW universe -- which is not
{\it a priori} obvious. It is also shown how to integrate these exact SS
equations, in cases where the data are not FLRW, and the space-time is not
known to be flat. It is essential for both flat and non-flat cases to have data
giving the maximum of the observer area (angular-diameter) distance, and the
redshift $z_{max}$ at which that occurs. This enables the determination of the
vacuum-energy density $\mu_{\Lambda}$, which would otherwise remain
undetermined.
