What is the ruling on one for whom it is difficult to lower his gaze from women who are not committed to Sharia, but he lowers his gaze from his female محارم (unmarriageable kin) in his home if they uncover themselves and exceed the limits of the legitimate 'awrah (body parts that must be covered) for a محرم?

A man must lower his gaze from unlawful things as much as possible. He should also strive to guide his unobservant female Mahrams towards modesty through an educational program that strengthens their faith, encourages them to do good, and warns them against evil, using texts from the two revelations (Quran and Sunnah). As for the link sent, it discusses the punishment of disbelievers, not lowering the gaze.