Trust is hard to earn but easy to lose. Unfortunately, there is no magic bullet for how to gain trust. What we do know is that we can only move forward, and that looking back and looking only at our failings does not give a true reflection of who we really are.
That is not to say that telling the truth isn’t important – it is! Rabban Gamliel, one of the great rabbis of early Jewish history, said that the world stands on, among other things, truth. The Torah tells us to stay far away from falsehoods. Interestingly, this is the only commandment in the torah where it says “stay far away.” Obviously it is important. But, the truth is that we all make the mistake of telling a lie. And when we do make that mistake, the important thing is what happens next.
In Jewish tradition, we understand that it is part of our job in the world to make mistakes. It doesn’t matter whether they are big mistakes or little ones, every person makes them. That is why the word for sin in Hebrew comes from an archery term meaning “to miss the mark.” We acknowledge that part of being alive is making mistakes. And it is not the mistakes that matter so much as what we learn from them and how we grow after we make mistakes. That is teshuvah – making a real change.
When we lie, we hurt people around us; those we lied to and those we lied about. We also make it hard for people to believe us again in the future, as your question acknowledges. But, if we make amends by apologizing and showing that we understand that what we did was wrong, we are already half way to starting the trust-rebuilding process. Maimonides says that what comes next is the most important step. When we are put in a similar situation we have to make a better decision. If we lied about doing our homework and the next time we are asked we tell the truth, and our teacher sees that we told the truth, then s/he can start to trust us again.
There are no easy answers to this question, but I believe that if you are making an honest effort, that people will respond. Trust, although hard to earn, can be earned. Even after it is lost.
Let's take the second question first. You seem to think that your obligation to tell the truth is linked to whether you will be believed. That is a faulty premise. Your obligation to tell the truth is unconditional, independent of whether you will be believed.
As to how you can earn or regain trust, there is guarantee you will ever regain that trust. You need to commit to telling the truth at all times. You need to ask yourself why you lied in the first place, and be able to answer the question honestly. Was it to cover up a theft, or a bad deed, a cheating of sorts? Did you put yourself into a position wherein you had no choice but to lie? Are you an habitual liar? These are serious questions you need to ask yourself.
The lie may be the end result of even more serious breaches. Whatever the case, you need to scrupulously avoid the circumstances that almost guarantee you will lie, and then you have to resolve that at all times, you will tell the truth even if it hurts you.
Those whose trust you want to earn or regain may never come around, as they may have been scorched too badly, or they may be the unforgiving type. Whatever the case, your focus needs to be on doing the correct thing. That IS in your hands. The rest is not in your hands. You can only hope the outcome, over time, will be as you desire.
Part of what it means to be Jewish is to own up to past mistakes and always try to do the "right thing." As the Torah tells us in the book of Deuteronomy (6:18), we should always try and do what is "straight and good in the eyes of God." Doing the right thing is sometimes difficult and can take a great deal of effort and courage on our part. Perhaps that is why the rabbis teach that a "hero" in Judaism is to be able to control our negative traits (Pirkei Avot 4:1).
So, what do you do if you lied to someone that you love and they no longer trust you? The first thing that you need to do is apologize for lying to them and ask for their forgiveness. Our tradition teaches that the only person who can forgive you for a wrong that you committed against them, is the person who was wronged. Once you have asked forgiveness, you can only hope to regain their trust by showing them that you have changed through your actions and words. It may take a while for them to trust you again, and they may not be so quick to forgive you- but while you cannot control their actions, you certainly can control yours by trying to do the right thing.
The question of "how" you can tell the truth after a lie if no one trust you is relatively simple. Whether or not someone trust you is irrelevant. It is always up to you strive to tell the truth. It may take some courage, but you can tell the truth simply by choosing to do so and following through. While there are a few exceptions- particularly when it comes to saving someone else from being embarrassed- Judaism teaches that we must always strive towards honesty in our interactions with others. In the end, our tradition reminds us that we must be able to go to sleep at night with a clean conscious and an honest soul.
One more thing- Never be afraid to admit that you do not know the answer to a question. The Talmud reminds us to teach our tongue to say, “I don’t know,” lest we invent something and be trapped (in a lie) (BT Berakhot 4a). If you can learn to say "I don't know" throughout life instead of making up answers to a particular question- you will be much better off.
Our Rabbi’s taught us about T’shuvah, which means repentance, or returning to the correct way to behave. T’shuvah is a process with many steps. When you make a mistake, like telling a lie to someone you love, the last part of the T’shuvah process is to make sure that you tell the truth the next time you are asked a question by that person (or anyone else!). The process of T’shuvah also includes admitting that you lied, both to yourself and to the person that you lied to, and telling them that you are sorry for lying to them. If you tell them that you understand what you did was wrong and that you will tell the truth next time, and if you really do tell the truth next time, then Judaism teaches that your loved one will forgive you. It may take time for them to trust you again but once they see that you are being truthful, and not lying anymore, you will be able to slowly rebuild their trust.