  The Balasin-Grumiller model has been the first model employed as an attempt
towards providing a fully general relativistic description of the dynamics of a
disc galaxy. In this paper, we compute the equatorial gravitational lensing
observables of the model. Indeed, our purpose is to investigate the role that
gravitational lensing plays as an observable in distinguishing between the
state-of-the-art galaxy models and the fully general relativistic ones, with
the latter stressing the role of frame-dragging and hence conceivably pointing
to a possible re-weighting of the dark matter content of disc galaxies. We
obtain for the Balasin-Grumiller model the exact formula for the bending angle
of light and we provide a corresponding estimate for the time delay between
images in the equatorial plane. For a reasonable choice for the values of the
parameters of the solution (bulge and scale radiuses, and average rotational
star speeds), the values that we obtain for the bending angle are in agreement
with those observed for typical disc galaxies. On the other hand, the
calculated time delay, which is directly tied to the frame-dragging generated
by the angular momentum of the galaxy, turns out to be some orders of magnitude
larger than the ones measured for the class of galaxies that the
Balasin-Grumiller model would claim to describe. We believe this abnormal
discrepancy to be due to the very nature of the Balasin-Grumiller model.
Namely, it being rigidly rotating, hence providing an unphysical amount of
frame-dragging. Therefore, we conclude that, in spite of its simplicity and its
unquestionable didactical value, the Balasin-Grumiller model is far too crude
to provide an instrument for a reliable general relativistic description of a
disc galaxy and that further work in the fully general relativistic modelling
of galaxies is required to reach a satisfactory stage.
