The 23-year old striker, who joined from Wolves at the end of January, marked just his fourth Scottish Premiership appearance with a treble of goals in Saturday's 5-0 win over Inverness and Lennon is looking for him to produce even more as he settles.
"I am delighted for him and he could have had a lot more over the course of the game," the Celtic boss said.
"His work-rate has always been good and his goal record is great. I think there's more to come from him in terms of his link-up play as well.
"He can play on his own. He's a very intelligent footballer and he can score individual goals.
"We saw a glimpse of what's ahead of us and I hope he thrives in the environment. It looks like he is enjoying himself."
"He's what we have missed up front since Gary Hooper left," Brown added.
"He's now getting those goals that 'Hoops' was getting for us. He's scoring hat-tricks and that's what we need. He's got a great left foot on him.
"He loves it here. He's Scottish, which always helps. He already knew a few of the lads, which has helped him settle in quickly as well. We've already seen what he has done in training and now it is shining in games."
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