The 19-year-old is a product of the Tottenham Hotspur academy and was most recently on the books at Wycombe Wanderers.
Hatters manager John Still told the official club website: "Lee is a youngster who we are giving a chance to because we feel he has some potential.
"We like him and his attitude. He's definitely one for the future."
Angol has previously enjoyed loan spells at Boreham Wood and Hendon.