If you are in a situation where players are lying about you and are not asking for reports then I really have no clue why this discussion is a discussion, other than because it hurt our feelings. In which case, again, I am sorry that this happened, no one deserves to be lied about. When players, or people in real life, are lying about you, its because they can not find a legit reason to talk poo about you to begin with. You should be PROUD they had to resort to a LIE, in order to try and get under your skin, because that shows that you are on the right Sportsmanlike path if not a better player than them as well. Muting them is your best option if you do not have the self discipline to ignore them without the MUTE button crutch.
An angry student walks up to his teacher, in class and challenges him to a duel. Shouting insults, "You're an old fool! You have no strength left! I will strike you down in one blow." But the teacher ignored him, and continued with his lesson, and when class was over the student left defeated with nothing. Another student approached the teacher when all the other students were gone and said, "Teacher, why did you not take his challenge, why did you let him insult you?"
The teacher responded, "If someone brings you a gift and you do not take it, To whom does it belong?" The student thought about it, and replied, "It belongs to the one who offered it." The teacher said, "It is the same with lies, envy and insults: If you refuse to accept them, they belong to the one who offered them."
Don't accept the toxic remarks other summoners make. Do not even respond to them. Anything offered and rejected, belongs to the person offering it.
You have NO power over others actions. Only power over how you react to them.
And as I said before, if a person resorts to a lie, in order to get a reaction of any sort, IT almost ALWAYS means they have nothing LEGIT on you. Be proud and focus on the fact that they have NOTHING legit on you, rather than zeroing in on the false statements they made.