  It is a long-standing open question if a gravitomagnetic charge, the
gravitational analogon to a hypothetical magnetic charge in electrodynamics,
exists in nature. It naturally occurs in certain exact solutions to Einstein's
electrovacuum-field equations with cosmological constant. The charged NUT-de
Sitter metric is such a solution. It describes a black hole with electric and
gravitomagnetic charges and a cosmological constant. In this paper we will
address the question how we can observe the gravitomagnetic charge using
gravitational lensing. For this purpose we first solve the equations of motion
for lightlike geodesics using Legendre's canonical forms of the elliptic
integrals and Jacobi's elliptic functions. We fix a stationary observer in the
domain of outer communication and introduce an orthonormal tetrad. The
orthonormal tetrad relates the direction under which the observer detects a
light ray to its latitude-longitude coordinates on the observer's celestial
sphere. In this parametrization we rederive the angular radius of the shadow,
formulate a lens map, discuss the redshift, and the travel time. We also
discuss relevant differences with respect to spherically symmetric and static
spacetimes and how we can use them to determine if an astrophysical black hole
has a gravitomagnetic charge.
