The Hoops manager is confident the youngster is fully focused on getting up to full speed - and staying fit.
Forrest could feature in their opening Antalya Cup match against Trabzonspor tomorrow night.
But the 22-year-old flew out to Turkey yesterday still waiting to hear if the Procurator Fiscal plans to proceed after he was reported for alleged incidents in a nightclub in Ayrshire in November.
Lennon is satisfied Forrest is handling the situation maturely, as he is showing by returning to form after suffering more sciatic and hamstring problems.
Referring to Forrest's off-field issues, the manager said: "I don't know where we are with that one, but it's certainly not affecting him in the way he is playing or training.
"I have not spoken to Jamesie about it. But I have spoken to his lawyer about things, and he is keeping us up to date with everything.
"So, we will cross that bridge when we come to it."
Lennon believes he saw a welcome glimpse of what Forrest can bring to the Celtic side when he played a pivotal role in overpowering St Mirren at the weekend.
He has been eased back into the side carefully since he returned from being out injured.
It has been the latest of a long list of frustrating lay-offs for the youngster, but Lennon hopes he is now growing out of his injury worries.
When asked how the club can get more out of him, and what will help him avoid the kind of injuries which have caused him to miss so many games, Lennon replied: "Hopefully, just the way his body changes as he gets older.
"He has had a long-standing sciatic problem. But, thankfully, for the last month or so, it has been all clear and he has got through the last two-and-a-half games unscathed.
"You can see that he needed the games, as did the other lads coming back from injury, Adam Matthews and Charlie Mulgrew.
"There's no question they make us better when they are in the side."
After working so hard in his rehab, the plan is to allow Forrest to train and relax in better conditions in Turkey.
However, Lennon has not ruled out the possibility of using the young winger in at least one of the two games they will play in the mini-
tournament involving Ajax, Trabzonspor and Galatasaray.
He explained: "We will monitor him and think about using him in a game.
"Or we may just do some fitness work and some technical work with him, just to keep him ticking over."