The 19-year-old has signed a two-year contract with the O's, and has the option of a further 12 months.
"I have had a great footballing education at Fulham, and I believe now is the right time to start my next chapter and kickstart my senior career," Gordon said.
"I'm really determined to make that transition into playing regular men's football and I am taking inspiration from people like Ollie O'Neill, who I know well from our time at Fulham together."
O's manager Richie Wellens added, "As a coach, it is refreshing to see a player turn down a Premier League contract to sign for a club in League One.
"That instantly tells you a lot about his character; it means he is hungry to do well.
"Lemar has good technical skills and he is someone we will put a lot of work into. We believe he has the potential to be a very good player for this club in the future."