The Argentine combined with Payet two years ago to score 22 goals and provide the same number of assists as the Hammers finished seventh in the league.
Arnautovic arrived from Stoke City in the summer, and after a rough start to life in the east end, has found his stride in the second half of the season.
And Lanzini is confident the duo can produce the goods for West Ham.
"Our partnership is fantastic," he told the club's website.
"It's easy to play with Marko because he is a good player, he has a good touch, good mentality and he wants to win the games. He is like me, so it's easy to play with these players.
"We make each other better, of course. We want the same things and we think the same way.
"It's similar to the feeling I had with Dimi before, because they are similar players. If you have a player who plays like you, it's easy. You need to connect and that's it. You touch the ball one way, and he touches the ball the same way."