  We revisit the relativistic restricted two-body problem with spin employing a
perturbation scheme based on Lie series. Starting from a post-Newtonian
expansion of the field equations, we develop a first-order secular theory that
reproduces well-known relativistic effects such as the precession of the
pericentre and the Lense-Thirring and geodetic effects. Additionally, our
theory takes into full account the complex interplay between the various
relativistic effects, and provides a new explicit solution of the averaged
equations of motion in terms of elliptic functions. Our analysis reveals the
presence of particular configurations for which non-periodical behaviour can
arise. The application of our results to real astrodynamical systems (such as
Mercury-like and pulsar planets) highlights the contribution of relativistic
effects to the long-term evolution of the spin and orbit of the secondary body.
