Mikael Lustig and Georgios Samaras found the net in the first-half for the Hoops before James Forrest added a third after the break to secure a commanding lead ahead of the home tie at Celtic Park.
Celtic had suffered some disappointing results in pre-season and Lennon felt his players produced a professional performance when it mattered.
"I'm delighted. We played well and scored three goals and created a lot of chances," he said.
"Hopefully we have a clean bill of health. It was a sticky game for us and we dealt with it very well.
"A lot of the talk has been about our pre-season and the results but we just wanted to try to get right for these games.
"Some are [getting sharper] and some are still quite rusty, which is totally understandable.
"But there were a lot of good performances. I'm delighted with the performance and the attitude of the team."
Lennon admitted it was an important night for him as he took Celtic back to his native Northern Ireland.
"It meant a lot to me personally, bringing a team back home," said Lennon.
"It was a special occasion and I wanted it to be right. I couldn't have asked for any more of the occasion. Both sets of supporters were brilliant."