Is saying "I will never do such and such again, O Lord" or "O Lord, I will not do such and such" considered a covenant, even without using the phrases "I covenant with You, O Lord" or "I promise You, O Lord"? And if it is a covenant, is expiation required if this act is repeated?

The phrases mentioned in the question are not considered a vow (عهد) that necessitates expiation (kaffarah) upon breaking it, unlike swearing by the covenant of Allah. A Muslim must lower their gaze from forbidden things and refrain from listening to sinful acts. They must fear Allah and repent from watching what is unlawful, for one who repents from a sin is like one who has no sin.