All three have been dual registered with Nottingham in the RFU Championship this season where they have helped the Midlands side with their push for promotion.
Stevens, 22, made his Tigers debut in January 2012, while 22-year-old prop Harris has made 10 first-team appearances since his debut in November 2009.
Winger Lewington, 21, scored his first senior try in the LV= Cup win at Harlequins last season and also started the semi-final victory over Bath.
London Irish director of rugby Brian Smith said: “[Forwards coach] Glenn Delaney has worked closely with these players and I’ve been impressed with what they’ve already achieved at Leicester and Nottingham.
“I’m sure we can develop them further and expect all three will be pushing for a place in our matchday squad. If they put their heads down, I have no doubt they can go on to higher honours.”