I thought I'd change the question around as it's always lower your gaze. Is there any situation where a man can look at a woman (meaning looking at her face primarily and wearing no face veil (Niqaab) if Muslim) but obviously not lustfully which maybe very hard if she is attractive to him and has makeup to enhance her beauty. Also she is outside the females whom he is prohibited to marry.
If there is not any kind of fitna and a good intention, there is nothing wrong to look into a face of a woman in public place such as hospital, if it is necessarily and short. But it is better not to look at all as it might create an uncomfortable situation. It is better always to lower your gaze. There is a hadith which is telling that a woman should be asked behind a veil something. This is to avoid any kind of fitna and Allah knows best.