  This white paper is the result of the Tri-Agency Working Group (TAG)
appointed to develop synergies between missions and is intended to clarify what
LSST observations are needed in order to maximally enhance the combined science
output of LSST and Euclid. To facilitate LSST planning we provide a range of
possible LSST surveys with clear metrics based on the improvement in the Dark
Energy figure of merit (FOM). To provide a quantifiable metric we present five
survey options using only between 0.3 and 3.8% of the LSST 10 year survey. We
also provide information so that the LSST DDF cadence can possibly be matched
to those of \emph{Euclid} in common deep fields, SXDS, COSMOS, CDFS, and a
proposed new LSST deep field (near the Akari Deep Field South). Co-coordination
of observations from the Large Synoptic Survey Telescope (LSST) and Euclid will
lead to a significant number of synergies. The combination of optical
multi-band imaging from LSST with high resolution optical and near-infrared
photometry and spectroscopy from \emph{Euclid} will not only improve
constraints on Dark Energy, but provide a wealth of science on the Milky Way,
local group, local large scale structure, and even on first galaxies during the
epoch of reionization. A detailed paper has been published on the Dark Energy
science case (Rhodes et al.) by a joint LSST/Euclid working group as well as a
white paper describing LSST/Euclid/WFIRST synergies (Jain et al.), and we will
briefly describe other science cases here. A companion white paper argues the
general science case for an extension of the LSST footprint to the north at
airmass < 1.8, and we support the white papers for southern extensions of the
LSST survey.
