However, it might be difficult for most people to orthogonalize these two components, since for them they occur simultaneously. That's the relevance of my asexuality to my comment: I suspect it allows me to experience the socio-emotional component without also experiencing the lust component, and thereby more easily see them as different.
If it's true that there's both a lust and socio-emotional component, it still seems inaccurate (or at least, idiosyncratic) to refer to the combination of the two as "lust".