  A method of general applicability has been developed, whereby the null
geodesic equations of the Einstein-Straus-de Sitter metric can be integrated
simultaneously in terms of the curvature constant $k$. The purpose is to
generalize the computation of light deflection and time delay by a spherical
mass distribution. Assuming a flat Universe with most recent measurements of
the Hubble constant $H_0$ and the cosmological constant $\Lambda$, five time
delays between the four bright images of the lensed quasar SDSS J1004+4112 have
been forecasted and compared to others in the field. In addition, we have
reviewed the question of the possible contribution of a positive $\Lambda$ to
reduce the light bending, and concluded that the changes are seemingly too
small to be appreciable on cosmological scales. The same conclusion has been
reached regarding the time delay. Having addressed the question of the effect
of the spatial curvature in both closed and open Universe, we have found that
the strong lensing is slightly affected by the expected small curvature density
$\Omega_{k0}$ of the current Universe within its error bar
$|\Omega_{k0}|\lessapprox 0.001$, in such a way that it may safely be
neglected. However, it's only if $\Omega_{k0}$ gets quite larger that the
effect being noticeable. While it is only theoretically possible for
$\Omega_{k0}$ to be higher, it's worthwhile to stress that this should impact
the light bending and time delay, causing them to decrease or increase
depending upon whether the spatial curvature is positive or negative.
Furthermore, one can infer that the observed light deflection and time delay
independently, that are found to be significantly deviated from those of the
flat Universe, may serve as a useful means to provide constraints on $\Omega
_{k0}$, thus making the approach employed in this work more promising than
others.
