The Hoops will face the Northern Ireland champions in the second qualifying round of the Champions League, with the first leg set to take place at Parkhead on July 16 or 17 before the return in Belfast.
Should they overcome Cliftonville, Celtic - who progressed to the last 16 last season - will need to get through two more qualifying rounds to reach the group stage. Lennon told the club's website: "It will be the first time I will have taken Celtic to a competitive game back home so that is something to look forward to."
He added: "But we will be totally motivated, obviously, to play as strongly as we can and try to win the tie. It's a great draw - a great draw for Cliftonville as well I would imagine. It will create a lot of interest back in Belfast but I am very wary of the tie.
"I know Gerard Lawlor, the chairman, very well and I know he will be absolutely delighted with the draw - and there will be a lot of familiar faces. We have three ties this year and our short-term priority will be to qualify for the group stages, which would mean a lot to everyone associated with the club. I'm not expecting us to have the same impact as last season but you just never know."
Cliftonville first-team coach Gerard Lyttle hailed the pairing with Celtic as a dream draw.
He told Press Association Sport: "We will be big underdogs and everyone will write us off but we will go there with a game plan and I just hope the players don't get stage fright.
"We didn't get together for the draw, there were lots of players working but with social media we all soon found out. It is everyone's dream. We had a good season, won the double and got pipped at the post for the treble so this is just the icing on the cake.
"When the draw was regionalised we knew we had a one in five chance of getting Celtic. We started pre-season on Saturday and will be working most of the week. I don't expect the treatment table to be full. Everyone will be buzzing."
The draw in Nyon, Switzerland also saw Welsh champions The New Saints drawn against Legia Warsaw, while Irish champions Sligo Rovers take on Molde, who are managed by former Manchester United striker Ole Gunnar Solskjaer.
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