Where can you enter Lemond serial numbers to figure out what year it’s made?

LeMond does not have such a database. The brand was owned by Trek in those years, so your best bet is probably just trying to find the appropriate year’s Trek catalog and compare.

This looks like a 2003 Buenos Aires. My dad had the exact same bike for years and was one of the first road bikes that I ever rode.

The frame is Reynolds 853 steel and is sturdy as hell but still such a comfortable ride. This bike should treat you really well if you keep it up—enjoy! Great find!