Despite scoring more goals domestically than any other team, Celtic have not had a natural striker in the team since Hooper left for Norwich in July 2013.
The Scotland international arrived from Wolves in the January transfer window, with some Celtic fans unsure of his credentials despite his 28-goal haul for Hibernian while on loan last season.
Griffiths has scored four goals in three Scottish Premiership games, and has won over some of his critics with his all-round performances.
Lennon was thrilled as the 23-year-old netted his first hat-trick for the Hoops on Saturday while setting up another goal in the 5-0 win over Inverness Caley.
"I am delighted for him and he could have had a lot more over the course of the game," the Celtic boss said.
"His first goal pleased me the most. We have been crying out for a penalty-box striker and that was a great ball and a great finish.
"He doesn't get disappointed (when he misses), he's hungry for more chances and he took his second and third goals brilliantly.
"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."