  In the near future, the overlap of the Rubin Observatory Legacy Survey of
Space and Time (LSST) and the Simons Observatory (SO) will present an ideal
opportunity for joint cosmological dataset analyses. In this paper we simulate
the joint likelihood analysis of these two experiments using six two-point
functions derived from galaxy position, galaxy shear, and CMB lensing
convergence fields. Our analysis focuses on realistic noise and systematics
models and we find that the dark energy Figure-of-Merit (FoM) increases by 53%
(92%) from LSST-only to LSST+SO in Year 1 (Year 6). We also investigate the
benefits of using the same galaxy sample for both clustering and lensing
analyses, and find the choice improves the overall signal-to-noise by ~30-40%,
which significantly improves the photo-z calibration and mildly improves the
cosmological constraints. Finally, we explore the effects of catastrophic
photo-z outliers finding that they cause significant parameter biases when
ignored. We develop a new mitigation approach termed "island model", which
corrects a large fraction of the biases with only a few parameters while
preserving the constraining power.
