The Hoops forward, top scorer at the club last season with 29 goals, opened the scoring in the 12th minute with a trademark poacher's finish before Raith skipper Allan Walker levelled in the 27th minute with a deflected shot from 20 yards.
However, Hooper, 24, minimised any chances of a cup upset when he restored Celtic's lead before the break before completing his scoring spree in the second half against the limited First Division side.
England goalkeeping coach Ray Clemence was up to watch keeper Fraser Forster in the Champions League game against Benfica last week and Celtic boss Lennon believes Hooper, who now has seven for the season, is entitled to some interest from Roy Hodgson.
The Northern Irishman said: "In Hooper we have a phenomenal player, not just his goals but his play in general was of a very high standard tonight. "If you look at his record, he does score a lot of goals and it is the hardest thing to do, and he scores in the big games. "He is a good footballer, an intelligent footballer, very quick over five or 10 yards, his touch is sublime at times. "He has led the line brilliantly for us this season and I think he is good enough to play for England. "At times he has had to play a little bit differently, particularly in Europe but all those aspects are building up to him being the all-round striker that he is.
"He thrives on goals, obviously, but his link-up play is fantastic and he is developing very well."
With a trip to Scottish Premier League leaders Motherwell on Saturday followed by a Champions League clash with Spartak Moscow in Russia next week, Lennon was glad to welcome back midfielders Beram Kayal and Joe Ledley, neither of whom had played since August due to respective ankle and groin injuries. Lennon admits he may have a "selection headache" in the upcoming games.
He said: "It was always the plan to give Beram an hour and give Joe half an hour so thankfully they came through that unscathed and will be fit for the weekend. "Lassad and Miku will be fit as well and Georgios (Samaras) isn't far away either so we are at almost at a full quota coming in to a big stretch of games." Rovers manager Grant Murray had no complaints about the result. He said: "It was always going to be a difficult task and when you go behind early it does make it an uphill battle but credit to the guys, they got themselves back in the game and probably had a chance after that. "But when Celtic get the second and third it does make it difficult. "But my players can come away from here heads held high, they gave it everything they had."