The Dutch manager will take in the Champions League game against Ajax on Tuesday, and Lennon believes van Dijk's displays have positioned him in the frame for an international call-up.
The 22-year-old has slotted into the Hoops defence with ease and has looked relatively comfortable in the Champions League for Celtic.
"Holland are a top, top team but for me he's been exceptional this season," said the Celtic manager. "He's got everything you want in a modern-day centre-half. He just gives us an extra dimension.
"His physical presence is great and unlike a lot of Dutch defenders he actually likes heading the ball.
"He's got a great spring and timing and he's been pretty dominant for us.
"He just needs to keep going and keep catching the eye. Certainly his performances in the Champions League will do that.
"I don't want to put any extra pressure onto him, but I think it is inevitable if he keeps going and progressing the way that he is just now that he will become a Dutch international.
"I just think he is a natural, a quality player.
"You could see it from his first day in training, or in the first game against Cluj in Germany.
"He makes it look easy. People seem to think he has a laid-back attitude, but his work ethic is very high and he's a kid who wants to get better. We've been delighted with him."
So far Van Dijk and Efe Ambrose have struck up a decent partnership, something that has become particularly important due to the long-term injury suffered by Steven Mouyokolo.
"They are quick, both of them," said Lennon with regard to Van Dijk and Ambrose.
"The idea was to have the three of them, him, Kelvin and Virgil.
"Obviously Kelvin left. We brought Steven in and we lost him to a really bad injury.
"Now the two of them have dovetailed very, very well - but we need to keep an eye on that."
Lennon believes that Celtic managed to snag a bargain when they landed van Dijk for £2.6million.
"I was over watching Ajax and they couldn't believe they had missed a trick with him," revealed Lennon, who will be back in Holland tonight to watch Tuesday's opponents play Twente in the Eredivisie.
"Even the English clubs as well. Because they have a lot of scouts in Holland, so maybe we have stolen a march on someone for a change.
"He has all the attributes to be a really top player."