The ESA Euclid mission is a space telescope that will survey ~15,000 square degrees of the sky, primarily to study the distant universe (constraining cosmological parameters through the lensing of galaxies). It is also expected to observe ~150,000 Solar System Objects (SSOs), primarily in poorly understood high inclination populations, as it will mostly avoid +/-15 degrees from the ecliptic plane. With a launch date of 2022 and a 6 year survey, Euclid and LSST will operate at the same time, and have complementary capabilities. We propose a LSST mini-survey to coordinate quasi-simultaneous observations between these two powerful observatories, when possible, with the primary aim of greatly improving the orbits of SSOs discovered by these facilities. As Euclid will operate from a halo orbit around the Sun-Earth L2 Lagrangian point, there will be significant parallax between observations from Earth and Euclid (0.01 AU). This means that simultaneous observations will give an independent distance measurement to SSOs, giving additional constraints on orbits compared to single Euclid visits.