I think that both love and lust exist, as two separate entities with an intertwined existence.
Both can exist without the other, and they can both exist simultaneously. Love is feeling for someone intellectually, liking them for their personality, their ideology, their connection to you or whatever else.
Lust is feeling for someone physically, liking them for their looks, or the way they carry themselves, or what have you.
That isn't to say that you can't love someone because of their looks, or that you can't lust for someone b/c of their intelligence - neither of them have bounds such as that. Usually [not always] though, lust is a want for stimulation (whether it be physical or mental) and love is a want for the lesser things - as simple as a smile, or a glance.
You love your siblings, your parents, your grandparents, and your friends - but it doesn't mean you lust for them, or that you ever will. You can lust after any number of people, but it doesn't mean you'll love them, or even know their name.
But you can love someone, and have that lead to lust; or lust after someone, and have love come to exist.
The line between the two is very fine and sometimes hard to distinguish; but they do exist as two different entities, even if they sometimes coexist in every way.