Bahai spirituality, universal law of love, page-8

No, lust and love is not the same vibrational energy, far from it.
Love is loving all equally, not loving your partner more than another, your chosen partner of love is because your vibrations match.
Lust is a type of ego, it is a low vibrational energy in a 3rd dimensional sense, God gives us free will to lust, but when you lust for another soul you focus on one soul only rather than the all, this can cause all kinds of vibrational problems of ego control and jealousy.