To answer this from a doctrinal perspective requires a doctrinal perspective on love. So we ought to turn to 1 Corinthians, chapter 13, Paul's famous homily on Charity (Christian love):
4 Charity suffereth long, and is kind; charity envieth not; charity
vaunteth not itself, is not puffed up,
5 Doth not behave itself unseemly, seeketh not her own, is not easily
provoked, thinketh no evil;
6 Rejoiceth not in iniquity, but rejoiceth in the truth;
7 Beareth all things, believeth all things, hopeth all things,
endureth all things.
By contrast, the word lust has a wider meaning than simply "unwholesome sexual desire." For example, from Mark 19, where Jesus explains the Parable of the Sower:
18 And these are they which are sown among thorns; such as hear the
word,
19 And the cares of this world, and the deceitfulness of riches, and
the lusts of other things entering in, choke the word, and it becometh
unfruitful.
We see "lusts" (plural) used here in the company of "the cares of this world" and being deceived (led astray) by seeking after riches. It speaks not of unwholesome sexual desire, but of unwholesome desires in general, not too different from gluttony or covetousness. The essence of lust is greed.
Contrast this greed with the attributes of Charity as described by Paul. Longsuffering, kindness, an absence of envy, ostentation and flashiness. "Not easily provoked," bearing and enduring all things with faith and hope. Distill all of these virtues down to their essence, and you get selflessness, the very antithesis of greed.
Greed is a hunger. It consumes in order to enlarge itself. But charity, pure Christian love, is selfless. It builds up those around it.
So how can this be applied to matters of the heart? What is the difference between real love, and lust?
Lust is greed. Lust says "this person is desirable, and I desire to have them, to further my own interests through interaction with them. I want to take pleasure from them, because it will make me feel good."
Love, on the other hand, is constructive. It says, "there is good in this person, and I want to work with them, to build something together with them that is greater and more beautiful than what either of us could accomplish alone, and I would wish to put forth the effort required to see it through, even if it requires some personal sacrifice on my part." Lust would never dream of that last bit!