Rhinos have released Lowes from his role as assistant-coach with immediate effect, allowing him to take up a new position outside rugby league.
Agar joined Rhinos last autumn as head of player and coach development – a role which did not include any first team coaching.
A former half-back with clubs including Featherstone Rovers and Dewsbury Rams, he was head coach of York City Knights, Hull, Wakefield Trinity and France and assistant to ex-Leeds boss Tony Smith at Warrington Wolves before spending a year in Australia.
Lowes returned to Rhinos last summer as first team coach and was assistant to current team boss Dave Furner before being released on Sunday.
The ex-Leeds player – who also coached Warrington and Bradford Bulls – is set to return to rugby union, where he has previous experience with Yorkshire Carnegie.
In a statement, Rhinos’ director of rugby Kevin Sinfield said: “On behalf of everyone at the Rhinos I would like to thank Jimmy for his efforts at the club.
“I know he is excited about the new challenge ahead of him and he leaves with our best wishes.”
Sinfield added: “In the interim, Richard Agar will join the first team coaching staff combined with his role as head of player and coach development.
“Richard is a vastly experienced coach and will be a great addition to the coaching staff.