The 21-year-old could make his debut for the Robins in Saturday's League Two clash with Northampton Town.
Cheltenham manager Mark Yates told the club's official website: "Lee is a player we have had an eye on for a while whilst he has been playing with Swansea's Under-21 side.
"He is a good player and a very good passer of the ball. We assessed the squad and he is something that we need so he is here to compete and play."
Lucas has not played a senior game for any team since making the only appearance of his loan spell at Burton Albion in January 2012.