The striker has been given permission to work on his fitness in the gym at Lennoxtown while he is home for the holidays.
Watt scored twice in Lierse's final game before their festive shutdown after coming on as sub against local rivals Mechelen.
Despite this, his future with the Belgian side he joined on a season's loan at the end of August, and where he has endured a difficult relationship with coach Stanley Menzo is still very much up in the air.
Watt was pictured warming up with the rest of the Celtic first team last week.
But Lennon has moved quickly explain the 20-year-old is not actually training with Scott Brown and Co. because, technically, he is a Lierse player and there would be issues if anything happened to him.
Lennon said: "Tony is still registered with Lierse until the end of the season. They can't send him back unless we take him back.
"He is using the gym facilities at Lennoxtown, but he is obviously not training with us because we can't run that risk. We will assess his situation as the month goes on."
Mo Bangura is due to report back to Lennoxtown today after completing his year-long loan with Elfsborg.
The Swedish club are not planning to take him back, either on loan again or on a permanent deal.
Celtic's first signing of this window, Holmbert Fridjonsson, is now
eligible to play but needs more fitness work before Lennon will consider pitching the 20-year-old Icelandic strike into the first-team squad.
So Bangura could find himself further down the Parkhead pecking order than he was when he left last January.
Lennon will turn his attention to Bangura's situation after he returns from the tournament in Turkey they are flying out next week to play in.
The Hoops boss wants to sign off before their mini-break with another win and clean sheet from their match against St Mirren on Sunday.
And, while Lennon is proud of the club's disciplinary record - they are top of the Fair Play league with the fewest bookings (22) in the first half of the SPFL Premiership season and not one red card-he would like them to have a bit more bite than they showed against Thistle on Wednesday.
Lennon said: "We do pride ourselves on discipline. The players conduct themselves well. What I would have liked to have seen on Wednesday was a little bit more aggression in our play at times.
"I thought we let the game run its course without really trying to affect it too much. That's something we need to look at for Sunday."
Meanwhile, Celtic Under-19s' side are taking part in a top five-a-side tourney in Germany next week.
The youths will go head-to-head against some of Europe's best young talent in the Sparkasse & VGH CUP 2014, which is based in the town of Gottingen.
Borussia Dortmund, Hamburg, Austria Vienna, Sparta Gottingen, JFV Northeim and SC Hainberg lie in wait in the young Celts' group, with the top four teams qualifying for the next round.