Yes I think it's very possible to go from Lust to Love.
All it takes is having one deep discussion to see some other value within the person. A lot of times this will happen if one person is having a problem and the other helps out in some way even if it's only listening. It opens a new the door.
However this may also lead to regret down the road.
There have been many times when people knew full well that the person they were having sex with was not "marriage material" or even "significant other" material from the beginning. Once they let emotiions come into the picture they find themselves trying to "change water into wine" and dealing with the frustrations that come with it. Not everyone is able to deal with having "booty calls" , "friends with beneifts" or "no strings attached" arrangements. They cross the line easily.
Going from Love to Lust is more of a challenge.
Most people are physically attracted or lust after a person they are interested in gettting to know. To love someone first means the relationship came about after a "friendship" was established. Most likely you didn't think of them as being "Hot". Odds are you never will think of them in that way no matter how much you love them. However it doesn't mean you can't have a passionate relationship.