The 20-year-old hitman arrives at the Sixfields Stadium having made three appearances for the Bees this season, scoring once in a Johnstone's Paint Trophy clash with AFC Wimbledon.
With a mounting injury list, Cobblers boss Aidy Boothroyd was happy to add to his depleted forward line.
"Luke is a centre forward who is strong and quick and we have watched him for a while," said the former Watford manager.
"He is one of those players on our under 21 list who we have done our homework on.
"With our injuries at the moment we need to add up front and I am sure he can come in and do a good job for us."