What is the ruling on looking at a woman without lust or the intention of inciting her, and what is the desired benefit of lowering the gaze in this case? And does the intended lust refer only to sexual lust, or does it include heartfelt love devoid of it?

Allah possesses ultimate wisdom in His decrees. There is no harm in a Muslim inquiring, seeking to understand the wisdom behind a legislation after accepting Allah's حكم (ruling), but the questioning must not be in a manner of objection. Islamic law has prohibited everything that leads to the unlawful and has blocked the means to it. Therefore, it commanded lowering the gaze completely from women - except for what is exempted, such as engagement (for marriage) - whether the gaze is with lust or without it, out of fear that an innocent gaze might lead to lust, and then to immorality, for Satan lures servants step by step. And whoever lowers his gaze in compliance with the words of Allah Almighty: "Say to the believing men that they cast down their gaze and guard their private parts; that is purer for them; surely Allah is aware of what they do," will achieve purity of the soul.