In short, yes, it's attached; but it's a complicated answer.
I think this is a case of lust having multiple definitions. For example, there is the biblical usage which frowns on the concept of having lust in is - but most people I know, myself included, do not interpret this kind of lust as simple sexual attraction. Rather it's a reference to desire that borders on obsession or which objectifies the other person and that is a bad thing.
But there is also modern-day usage of the word that simply refers to being strongly attracted to someone in a sexual way, desiring them physically, etc. And that is simply biological nature.
So I would answer, yes, wanting to have sex with someone is lusting after them, but that this isn't inherently a bad thing.