"I no longer lover her" and "I don't love her anymore" mean the same thing. The difference is the level of language. "I no longer love her" is more formal English than "I don't love her anymore" which is more colloquial. Other examples (with the same difference of formal versus colloquial): I no longer eat eggs for breakfast. I don't eat eggs for breakfast anymore. He no longer lives with his mother. He doesn't live with his mother anymore. The difference is even more pronounced (that is, formal versus informal) when used in the affirmative: He has long been a friend of mine. He has been a friend of mine for a long time.

Both phrases say the same thing in different ways. You could also say: " I'm not in love with her anymore." "My love for her is no longer there." It is your choice. I feel that the most casual and natural way someone would say that would be, " I don't love her anymore."