I don't think I have ever seen a LIDAR vacuum for under $250. From my research, the cheapest, reputable LIDAR vacuum is the WYZE for ~$300USD:
https://www.wyze.com/products/wyze-robot-vacuum
Otherwise, the Eufy L70 is a little more expensive but does include a mopping pad.
https://www.amazon.com/eufy-Navigation-Sweeping-Self-Charging-Hardwood/dp/B07RDFFSJC
EDIT: The Eufy seems to be on sale and there is a "renewed" version on sale for about $250 that would get into your budget.