What is the ruling on the promises I made to myself to abandon some sins, such as lying and lowering the gaze? Am I obligated to fulfill them despite the difficulty of adhering to them in society?

Breaking a promise to Allah may cause hypocrisy to enter the heart, as Allah Almighty says: "And among them are those who made a covenant with Allah, [saying], 'If He should give us from His bounty, we will surely spend in charity, and we will surely be among the righteous.' But when He gave them from His bounty, they hoarded it and turned away, while they were refusing. So, He put hypocrisy into their hearts until the Day they will meet Him, because they broke their promise to Allah and because they used to lie." The remedy for this is to be mindful of Allah, to believe that He knows all secrets and private counsels, and to seek Allah's help to remember Him, thank Him, and worship Him well.