Lust is generally defined as the desire for another person on a physical level. Love is generally thought to include more than just physical attraction and desire. Love at first sight is usually spoken of by people later on in their relationship. What they really experienced was more likely lust than love. However, when they look back on their relationship, they recognize the initial attraction and associate it with their later feelings of love. 

Love at first sight is real, but it is a combination of physiological and emotional factors that vary from person to person.  Part of it is based on the romantic idea we have in our society about love at first sight.  The love that's important is the love that lasts.  Sometimes that can be based on instant attraction, but by definition that attraction can only be physical.  Attraction should be more than skin deep!

You can have love and lust separately, or they can occur together. Lust is a biological state; it's your brain responding to hormones that your body is creating. Lust is what drives the desire for sexual relations.

Love is a psychological state. It is created in the brain, though it affects the body as well. Love is usually tolerant and long-lasting, whereas lust is a temporary state and is purely physical. Sometimes lust leads to love, but more often not.

A short way to say is it that lust is in your body, love is in your mind.

Lust is physical attraction with minimal concern for anything other than satisfying that basic instinct.

Love may include lust, but also involves caring about the partner, concern for the partner's wellbeing, commitment to sharing time and events and activities and hopes and disappointments with the partner.

Lust is a hormone induced state that is temporary and often beyond our conscious control. We can choose not to act on lust, but it's difficult not to experience it, whether we want to or not.

Love is more of a decision that one makes to care for someone in a committed sense that is practical as much as emotional. Hence the wedding vows in which we promise to take care of each other.

Lust is a part of romantic love.  I don't think that you can have romantic love without some element of lust.  However, lust is "just" a physical feeling.  It can occur outside of romantic love.  I think that lust is enhanced by love, though.  I think that you feel more lust for a person if you are in love with them as well.

If you define lust as physical desire and love as something deeper, then it would be logically impossible to experience love at first sight, since the only impression you have of a person at first sight is their physical appearance.