  Along their path from source to observer, gravitational waves may be
gravitationally lensed by massive objects. This results in distortions of the
observed signal which can be used to extract new information about fundamental
physics, astrophysics, and cosmology. Searches for these distortions amongst
the observed signals from the current detector network have already been
carried out, though there have as yet been no confident detections. However,
predictions of the observation rate of lensing suggest detection in the future
is a realistic possibility. Therefore, preparations need to be made to
thoroughly investigate the candidate lensed signals. In this work, we present
some of the follow-up analyses and strategies that could be applied to assess
the significance of such events and ascertain what information may be extracted
about the lens-source system from such candidate signals by applying them to a
number of O3 candidate events, even if these signals did not yield a high
significance for any of the lensing hypotheses. For strongly-lensed candidates,
we verify their significance using a background of simulated unlensed events
and statistics computed from lensing catalogs. We also look for potential
electromagnetic counterparts. In addition, we analyse in detail a candidate for
a strongly-lensed sub-threshold counterpart that is identified by a new method.
For microlensing candidates, we perform model selection using a number of lens
models to investigate our ability to determine the mass density profile of the
lens and constrain the lens parameters. We also look for millilensing
signatures in one of the lensed candidates. Applying these additional analyses
does not lead to any additional evidence for lensing in the candidates that
have been examined. However, it does provide important insight into potential
avenues to deal with high-significance candidates in future observations.
