We present results from the Large Adaptive optics Survey for Substellar Objects (LASSO), where the goal is to directly image new substellar companions (<70 M$_{Jup}$) at wide orbital separations ($gtrsim$50 AU) around young ($lesssim$300 Myrs), nearby (<100 pc), low-mass ($approx$0.1-0.8 M$_{odot}$) stars. We report on 427 young stars imaged in the visible (i) and near-infrared (J or H) simultaneously with Robo-AO on the Kitt Peak 2.1-m telescope and later the Maunakea University of Hawaii 2.2-m telescope. To undertake the observations, we commissioned a new infrared camera for Robo-AO that uses a low-noise high-speed SAPHIRA avalanche photodiode detector. We detected 121 companion candidates around 111 stars, of which 62 companions are physically associated based on Gaia DR2 parallaxes and proper motions, another 45 require follow-up observations to confirm physical association, and 14 are background objects. The companion separations range from 2-1101 AU and reach contrast ratios of 7.7 magnitudes in the near infrared compared to the primary. The majority of confirmed and pending candidates are stellar companions, with ~5 being potentially substellar and requiring follow-up observations for confirmation. We also detected a 43$pm$9 M$_{Jup}$ and an 81$pm$5 M$_{Jup}$ companion that were previously reported. We found 34 of our targets have acceleration measurements detected using Hipparcos-Gaia proper motions. Of those, 58$^{+12}_{-14}$% of the 12 stars with imaged companion candidates have significant accelerations ($chi^2 >11.8$), while only 23$^{+11}_{-6}$% of the remaining 22 stars with no detected companion have significant accelerations. The significance of the acceleration decreases with increasing companion separation. These young accelerating low-mass stars with companions will eventually yield dynamical masses with future orbit monitoring.
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