Does one know why looking at a non-mahram woman is forbidden?

A believer must submit to Allah's command, whether they understand its wisdom or not. The wisdom behind forbidding looking at foreign women is clear: it closes the door to temptation, which is a great danger. Islamic law has taken precautions in the relationship between men and women by establishing boundaries and etiquettes that ensure chastity and preserve the purity of hearts. Among these is the command to lower the gaze, as stated in the Almighty's words: "Tell the believing men to reduce [some] of their vision and guard their private parts. That is purer for them. Indeed, Allah is Acquainted with what they do." Looking invites corruption of the heart and is one of the impulses for lust. The Shariah has closed this door so that one does not seek to fulfill lust outside of the Sunnah.