  We investigate autonomous perturbations on the orbits of LISA, namely the
effects produced by fields that can be expressed only in terms of the position,
but not of time in the Hill frame. This first step in the study of the LISA
orbits has been the subject of recent papers which implement analytical
techniques based on a "post-epicyclic" approximation in the Hill frame to find
optimal unperturbed orbits. The natural step forward is to analyze the
perturbations to purely Keplerian orbits. In the present work a particular
emphasis is put on the tidal field of the Earth assumed to be stationary in the
Hill frame. An accurate interpretation of the global structure of the perturbed
solution sheds light on possible implications on injection in orbit when the
time base-line of the mission is longer than that assumed in previous papers.
Other relevant classes of autonomous perturbations are those given by the
corrections to the Solar field responsible for a slow precession and a global
stationary field, associated to sources like the interplanetary dust or a local
dark matter component. The inclusion of simple linear contributions in the
expansion of these fields produces secular solutions that can be compared with
the measurements and possibly used to evaluate some morphological property of
the perturbing components.
