What is the ruling on looking at non-Muslim women—such as their hair—without lust? And is the obligation to lower one's gaze restricted to Muslim women only?

Allah has commanded the believers to lower their gaze, and this includes looking at both Muslim and non-Muslim women. The reason for this is to block the means (to sin) and prevent temptation, and this temptation exists when looking at a non-Muslim woman. Imam Malik disliked looking at the hair of non-Muslim women (from the People of the Book). The permissions reported from some of the early Muslims in this regard are likely to be interpreted as referring to female slaves. Non-Muslims are addressed by the ancillary rulings of Sharia, and a non-Muslim woman is commanded to cover her hair and awrah (private parts). There is no differentiation in the texts between a Muslim woman and a free non-Muslim woman in the matter of lowering the gaze.