Lilley, 21, has yet to play a competitive game for Rhinos this season.
He was named in their initial 19-man squad to face Catalans Dragons last week, but the game was postponed and Lilley lost his place to fit-again full-back Jack Walker for Thursday’s visit of Hull.
The Leeds-born play-maker is in contention to make his Leigh debut in Sunday’s Betfred Championship fixture at Halifax.
Lilley made his first appearance for Leeds away to Wakefield in June, 2015. He has scored three tries and 51 goals in 37 first team games, but was restricted to only nine matches for Rhinos last year and played another 12 on loan at Bradford Bulls
Leigh have won only one of their five Championship games this season and were beaten 38-30 at home by Featherstone Rovers last week.
Centurions chairman Mike Latham said: “When you are in a circle of negativity results-wise it is hard to break and Jordan’s signing gives everyone at the club a big boost.
“With Ben Reynolds being injured last weekend we had an urgent need for a half-back and we would like to offer our sincere thanks to [chief executive] Gary Hetherington and [coach] Brian McDermott at Leeds Rhinos for allowing Jordan to join us.”
Latham added: “If things work out favourably for all parties there is a possibility the loan deal can be extended.
“Jordan is a talented young player who has already got a lot of first team experience under his belt and I am looking forward to seeing him play in the Leigh Centurions jersey.
“Hopefully a large number of our supporters will be making the trip to Halifax on Sunday to cheer on Jordan and the boys as we look to get our season back on track.”
Lilley signed a three-year contract last July, keeping him at Leeds until the end of 2020.
Rhinos have a dual-registration agreement with Featherstone, but Rovers have a settled half-back pairing of Martyn Ridyard and Tom Holmes.