Full-back Lustig has struggled to make an impact at the Glasgow club since arriving from Rosenborg in January.
The Swede was hampered by injury and was fortunate to make his national squad for the European Championship finals this summer.
However, the 23-times capped defender is now hoping to play against England, France and Ukraine. And he believes being involved will help him enormously when he returns to Scotland to play for the Hoops next season.
He said: "Since my move to Celtic, I've been up and down. I was really hurt all of January and February and then I've only been playing sporadically after that. Since I was used to playing every week, this has been a new experience for me.
"I don't want to take away the achievements of the other players in my position, but if I had been fit, I would have definitely played in more matches.
"I was worried that I wouldn't get picked for the Euros and it was a relief when I was included. I really like Glasgow and we have a great flat there.
"Celtic are a big club and the players in the team are really good to me. And I hope to play a bigger part next season."
Lustig is itching to get involved in his first major tournament – and is hopeful his team can overcome England in their group game.
He said: "It's always been my dream to play for Sweden at the finals of a tournament.
"England are obviously favourites in the group, along with France.
"But we have a good record against them and I do not think it is clever to throw in a brand new coach (Roy Hodgson) as close as this to the European Championships. They have not had time to get used to him."