"Can a another yandere take Yuno's throne?"

Well yes. But it'll be hard, you see. Yuno was a successful yandere, she got Yuki and lived a happy life, being a yandere is too kill whoever stands in their way, but at the same time, ACTUALLY getting their "Senpai". Shion failed, and lost her life, and the Yangire won, Rena. 
Ayano is currently different, she's struggling from LITERALLY trying to get senpai to notice her, I mean c'mon, most power yandere, is supposed to be successful, not just dangerous.
You need a yandere, who got their senpai, and killed multiples, but at the same time, was very strong.
Yuno also had high intelligence, and was very smart, and as we know, intelligence defeats strength in the human race.

"Can Ayano defeat Yuno?"

You serious? That's like asking if Jackie Chan can defeat Bruce Lee. No, not so easily. Yuno is a straight A student, high intelligence and remarkable speed and endurance, with inhuman senses. Ayano only has Yandere vision, and is a learning yandere, with the easter eggs however, then Yuno should be given her god powers to even the fight.

"Can Lucy defeat Yuno?"

She could, but I remember seeing a fight, between Lucy and a relative. Yuno is a smart girl, she CAN keep her distant, and use firearms, and/or throw melee weaponry, and she can dodge. It's another battle between brain vs muscle, and Yuno has the brains, I've seen the fight, keep your distance, dodge, and use what you got. Yuno still has a good chance of winning

Those are currently the questions i had.
Got a question to ask?
Leave it down in the comments, and I'll be more than happy to answer
Have a nice day, and thanks for reading.