After strikes from
He saved the striker's close-range header, having earlier kept out
Lassad was replaced by
"He hadn't played for three or four months and we always worried that fitness would be an issue," said Lennon.
"He came off with a slight groin problem but we are hoping that it is just a mild problem.
"His link-up play was good, he won us the penalty, he had a really good header tipped over the bar so we were pleased in general with his play and we know there is more to come from him."
The champions' superiority could have translated into more goals had it not been for some wayward shooting and a fine performance by Douglas.
Brown's penalty was well struck but the 40-year-old Dees number one got a hand to the ball to tip it over.
Celtic has struggled from the spot under Lennon and the Northern Irishman admits there might be a change in taker for the next one it is awarded.
Lennon said: "Scott has been the designated taker for quite a while and this was the first penalty of the season.
"So there might be a bit of a queue lining up to take the next one."
Dundee remains bottom of the table with four points from seven games and it looks like being a long season for the Taysiders.
As runner-up to Ross County in the Irn-Bru First Division last season,
Smith tried to put a sheen on what had been a comfortable win for the home side. The former Celtic defender said: "The positives were that we created chances against Celtic and for the majority of the game we defended well against a good Celtic team.
"So we have to remain positive. We have a good set of boys in that dressing room and we just need a wee bit more belief at times.
"I think we started the game very well and created a few chances.
"We lost two goals at bad times, just before half-time and just after so it was a real uphill struggle to get back in the game.
"It is easy at Parkhead to buckle at 2-0 and so I am pleased that the boys stuck at it, they refused to lie down and kept working hard."
Australia midfielder Tommy Oar celebrated his Socceroos call-up with a starring role in FC Utrecht's 2-0 win at Twente in the first leg of their UEFA Europa League play-off.