Have I committed a sin or an offense by not paying attention to my aunt in the means of transportation? And how is the correct lowering of the gaze done without falling into a wrong understanding, especially since it is permissible to look at one's Mahram? And how can one differentiate between women to lower the gaze from non-Mahram women?

Lowering the gaze from what is forbidden is obligatory, as Allah the Almighty says: "Tell the believing men to lower their gaze." It is necessary to avoid looking at non-mahram women, and if a glance occurs by mistake, it is obligatory to avert it, as the Prophet, peace and blessings be upon him, said to Ali: "Do not follow a glance with another, for the first is yours but not the second." And concerning the sudden glance, he said: "Avert your gaze." It is not permissible to let one's gaze wander among women in search of aunts (maternal or paternal), for warding off harm takes precedence over gaining benefits. Lowering the gaze preserves one's chastity, purifies the soul, strengthens the heart, and brings about the sweetness of faith. One can search for an aunt through other means, such as calling out or asking.