  In globular clusters, dynamical interactions give rise to a population of
eccentric double white dwarfs detectable by the Laser Interferometer Space
Antenna (LISA) up to the Large Magellanic Cloud. In this Letter, we explore the
detectability of periastron precession in these systems with LISA. Unlike
previous investigations, we consider contributions due to tidal and rotational
distortions of the binary components in addition to general relativistic
contributions to the periastron precession. At orbital frequencies above a few
mHz, we find that tides and stellar rotation dominate, opening up a possibly
unique window to the study of the interior and structure of white dwarfs.
