About Hermas, whether he was supposed to have desired the woman in a sexual or nonsexual manner isn't specifically stated. He may have been justifying himself in his own mind in that story. It did cause me to think of the issue of nonsexual lusting when I wrote it.
In English, we use the word 'lust' in an exclusively sexual sense. The Biblical use of the term seems to refer to illegitimate desire, and Paul associates it with the command 'thou shalt not covet.' The word often seems to be used to refer to sexual lust though. But a man coveting his neighbor's wife for her apple pies is still coveting, and he is giving in to some kind of lust, IMO.
Btw, I think there is a difference between lusting and coveting, since 'when lust hath conceived, it brings forth sin.' Lust brings forth sin. It is not sin. Lust conceives sin if we yield to the lust. Paul says not to yield your members into sin. Yielding to lust can be ask simple as yielding the eyes.
What if it goes a step further and he says to himself, "I wish she were my wife"? He could do this without having sexual thoughts.