It is a serious sin not to carry out one’s duties and responsibilities knowing well that they are such.
“He who does not do the good knowing it, is guilty of sinning” (James 4:17).
In the parable of Lazar no explicit reason is given for the richman’s condemnation into hell. But he is guilty of omission. He could have easily helped Lazar to make a living, which he didn’t do. That was why he was punished.
St.Basil says, “The food set apart for the next day in one’s cupboard is the rightful share of another, who is without food today”. Hence it is a sin not to do a good thing within our power.
“Away with you, you cursed ones, into the eternal fire prepared for the devil and his demons. For I was hungry, and you wouldn’t feed me; thirsty and you wouldn’t give anything to drink; a stranger, and you refused me hospitality; naked, and you wouldn’t clothe me; sick and in prison, and you didn’t visit me. They will reply: Lord, when did we ever see you hungry or thirsty or a stranger or naked or sick or in prison? And I will answer, ‘When you refused to the least of these my brothers, you were refusing help to me” (Matthew 25:41-45).
So beware of the sins of omission.