  Gamma strength functions (GSFs) and level densities (LDs) are essential
ingredients of statistical nuclear reaction theory with many applications in
astrophysics, reactor design, and waste transmutation. The aim of the present
work is a test of systematic parametrizations of the GSF recommended by the
RIPL-3 data base for the case of $^{208}$Pb. The upward GSF and LD in
$^{208}$Pb are compared to gamma decay data from an Oslo-type experiment to
examine the validity of the Brink-Axel (BA) hypothesis. The E1 and M1 parts of
the total GSF are determined from high-resolution forward angle inelastic
proton scattering data taken at 295 MeV at RCNP, Osaka, Japan. The total LD in
$^{208}$Pb is derived from the $1^-$ LD extracted with a fluctuation analysis
in the energy region of the isovector giant dipole resonance. The E1 GSF is
compared to parametrizations recommended by the RIPL-3 data base showing
systematic deficiencies of all models in the energy region around neutron
threshold. The new data for the poorly known spinflip M1 resonance call for a
substantial revision of the model suggested in RIPL-3. The total GSF derived
from the present data is larger in the PDR energy region than the Oslo data but
the strong fluctuations due to the low LD resulting from the double shell
closure of $^{208}$Pb prevent a conclusion on a possible violation of the BA
hypothesis. Using the parameters suggested by RIPL-3 for a description of the
LD in $^{208}$Pb with the back-shifted Fermi gas model, remarkable agreement
between the two experiments spanning a wide excitation energy range is
obtained. Systematic parametrizations of the E1 and M1 GSF parts need to be
reconsidered at low excitation energies. The good agreement of LD provides an
independent confirmation of the approach underlying the decomposition of GSF
and LDs in Oslo-type experiments.
