For instance, say we tell an insignificant lie that doesn’t really affect another person. A day or so passes, and we don’t admit to it. Are we obligated to bring up this lie to the person, or can we simply pray and strive to avoid lies in the future?
Honesty is not the only virtue. Use wisdom and Prudence. Why make your life worse than it has to be? Unless it is absolutely necessary to be honest about the white lie, forget it and move on. Is it honesty or are you talking about lying about an opinion? I think people give their opinions way too much these days. Lying that a dress looks OK on someone will not condemn you to hell. Besides, that is a matter of opinion anyhow.
If it’s going to impact them negatively unless corrected, then you should admit it. (If you told them Thanksgiving was at Grandma’s when it’s at Aunt Carol’s, you’d want to correct it. [Just like if it were an hobest mistake.] But if telling them the truth would be hurtful in itself like the dress scenario, don’t bother.)
There does not appear to be a definitive obligation to admit to wrongs (to the wronged party) or make restitution or submit to civil authorities. [One can debate what the exhortation to Love one’s neighbour might require - but such precepts are directional, not absolute.]
For example - if one commits a serious offence, say, a murder - and genuinely confesses this sin - one might imagine the priest absolving you of the sin and nominating a penance such as “present yourself to the police”. This does not happen.