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2 May 2019, 11:06
It means he will almost certainly miss Scotland's European Championship qualifying double-header in June.
There were fears the left-back would miss the rest of the season after being left out following the 3-0 William Hill Scottish Cup semi-final over Aberdeen last month.
However, he is in contention for the Ladbrokes Premiership clash with the Dons at Pittodrie on Saturday where a point will clinch an eighth successive title for the Parkhead side.
Tierney will go under the knife after Celtic play Hearts in the William Hill Scottish Cup final on May 25 with Scotland facing Cyprus at Hampden Park on June 8 before travelling to Belgium three days later.
"He has had advice from the specialist and we are just going to manage him through until the end of the season hopefully," said interim boss Lennon, who confirmed the club had triggered a 12-month extension clause on winger Scott Sinclair's contract.
"I think it will be very difficult for him to go with Scotland.
"We have sort of managed him on a daily basis and he is going to require surgery and the sooner the season finishes and he gets surgery the better it will be for him going forward and (the timescale) is probably three to four weeks.
"That is the idea. It is a double hernia, so that needs fixing."
Lennon, who also revealed striker Leigh Griffiths is back training after being out since December with personal problems although still short of being included with the squad, believes the retention of Sinclair is significant.
The 30-year-old, who signed from Aston Villa in 2016, has scored 17 goals this season.
He said: "Scott will be here for another year. He has been a good player since he walked in the door.
"He has made a big contribution in the goals column and that football intelligence and experience is always important to have around.
"There is a familiarity there for Scott going into the Champions League qualifiers next season, and he is one that we don't have to replace.
"He has played a lot of games this season. Under me he has played maybe 75/80 per cent of the games.
"He maybe hasn't hit the heights of the first season but that was a stellar season and it is very difficult to replicate that year on year.
"But we know that Scotty is an excellent players and always a threat."
Lennon is happy to see the return of Griffiths after a fitness assessment last week.
He said: "It went well. He is running on the grass and doing a little more conditions work.
"He is making good progress..
"He has another couple of weeks of work before we can throw him in with the rest of the squad."