The Portland Trail Blazers point guard averaged 20.7 points per game during the 2013-14 regular season and 22.9 during the playoffs, but has less than a block and a steal per game during his career.
Payton told CSNNW.com: "He can be like Patrick Beverley [of the Houston Rockets] if he wants to, but that's a mindset.
"I think Damian has to be willing and ready to play that type of way. Right now, he's scoring so easily and he's so good at the offensive end, he doesn't have to think about defense. He doesn't have to think about it because he knows he can outscore somebody.
"He can have 35 [points] when he wants to and that's where the game is going right now. But we have to get that out his mindset. If he wants to be a two-way guard and have his name in a legacy for being that way, he has to step it up on the defensive end."
Lillard was the sixth overall pick in the 2012 Draft.