When we talk about romantic relationships, sometimes we decide to use general and ambiguous words. For example:
Hay otro en su vida. [There is another in her life]
In this case "another" means "a man with whom she has a second relationship, probably a lover or a substitute."
Creo que con María tenemos algo. [I think we have something with Mary]
In this case, "something" means "a romantic relationship".
Entre nosotros no hay nada. [Between us there is nothing]
Here, "nothing" means "no type of love relationship".
Por fin Andrea está con alguien. [Andrea is finally with someone]
And here "is with someone" means "having an affair with a man."
I do not know if these examples show some kind of universal phenomenon, or is only in Spanish. But I think that being ambiguous in our language we are trying to give the message an "atmosphere" of privacy, confidentiality and discretion.
So answering your question, "hay otro en mi vida" can mean "I have a lover" or "I'll change you by another guy/girl."