  We present an in-depth characterization of the polarimetric channel of the
Large-Angle Spectrometric COronagraph/LASCO-C3 onboard SOHO. The polarimetric
analysis of the white-light images makes use of polarized sequences composed of
three images obtained through three polarizers oriented at +60$^\circ$,
0$^\circ$, and -60$^\circ$, complemented by a neighboring unpolarized image.
However, the degradation of the 0$^\circ$ polarizer noticed in 1999 compelled
us to reconstruct the corresponding images from the other ones thereafter. The
analysis closely follows the method developed for LASCO-C2 (Lamy, et al. Solar
Physics 295, 89, 2020 and arXiv:2001.05925) and implements the formalism of
Mueller, albeit with additional difficulties notably the presence of a
non-axially symmetric component of stray light. Critical corrections were
derived from a SOHO roll sequence and from consistency criteria (e.g., the
tangential direction of polarization). The quasi-uninterrupted
photopolarimetric analysis of the outer corona over two complete Solar Cycles
23 and 24 was successfully achieved and our final results encompass the
characterization of its polarization, of its polarized radiance, of the
two-dimensional electron density, and of the K-corona. Comparison between the
C3 and C2 results where their field of view overlaps shows an overall
agreement. The C3 results are further in agreement with those of eclipses and
radio ranging measurements to an elongation of about 10 solar radii but tend to
diverge further out. Whereas the coronal polarization out to 20 solar radii is
still highly correlated with the temporal variation of the total magnetic
field, this divergence probably results from the increasing polarization of the
F-corona.
