The winger joined Sundowns in August after a nine-year stay with PSL rivals Kaizer Chiefs.
Lebese's talent is undeniable but the 28-year-old has been dogged by inconsistency, something he hopes to remedy at Chloorkop.
"I think here we can share the load and, like I've said, there's a lot of great players so I feel I can also rise to their level," he told the October edition of KICK OFF Magazine.
"When you're surrounded by great players you also adopt that quality, so I'm hoping to kick on quickly. I'm just hoping to get up to speed with the rest of the team."
The 28-year-old added: "I need to stick to the principles of the team and what is required of me, and I always need to be a step ahead, taking into account my game, that of the team, and the opponents. It's one game at a time and I know what is required of me."
Lebese will come up against Chiefs for the first time tonight and sees no reason why he should not celebrate if he scores against the Soweto giants at Loftus Versfeld.
For more from Lebese on his reasons for leaving Amakhosi, working with Pitso Mosimane and his ambitions, get the October edition of KICK OFF Magazine, on sale now! Prefer reading KICK OFF Magazine on screen? DOWNLOAD a digital copy of the magazine here!