The goalkeeper made his full international debut in a 2-0 friendly defeat to Chile last Friday.
Lennon told Celtic TV: "I'm very proud of him.
"And it's great for the club. In this day and age and all the negative things that get thrown at the Scottish game, to think we have an England international in the ranks.
"It's a very proud time for the club and player and it's testament to the dedication and commitment he has shown in the last three years and the improvement he has made in his game.
"I don't want it to be a short-term thing, I want him to be in and around for the next three, four or five years or however long it's going to be."
Forster is one of five Celtic players who are currently in the squads of countries going to next year's World Cup.
Nigeria defender Efe Ambrose, Honduras left-back Emilio Izaguirre, Greece forward Georgios Samaras and Australian midfielder Tom Rogic also look sure to be heading for Brazil next summer.
Lennon said: "It speaks volumes for the scouting network and the players we have brought in and all the hard work behind the scenes."
- Sports & Recreation