That depends on what you lied about, and why and how.
you should try to gain your trust back by maybe telling the truth so next time she needs you she doesnt find out that you lied.
What if your boyfriend doesn't believe what you say because you lied to him once? what should I do? Was your boyfriend trusting and good before you lied? Was the thing you lied about big enough to warrant his mistrust? If you lied to him about something big, or if you have a habit of lying to him about things, then you need to earn back his trust. If you broke his trust then it is yours to fix. If, however, you lied to him about whether or not you ate the last piece of pie and he says he cannot trust you, then you may need to reevaluate whether or not you are with a quality person.
You only be lied to if you listen. Drop the lier.
You don't. You have to let him decide when or if he forgives you at all. Once trust is broken, it's very difficult to get it back.
Sometimes it takes more then words to gain someone's trust. If you have lied once, people have a tenancy of categorizing you into the list of people who always lie.
It's easy for someone to just get your trust back rather than work for it. I think she should earn it back. Have her show to you that she is worth keeping as a friend and prove she can be honest as well as a good friend.
There is no "way" to trust someone. Once trust is broken, nothing but time& security will fix it.
Be very nice to her and next time you have the chance to tell the truth, do so. Women are very fragile, like a vase. Treat her with delicacy. Soon you will earn back her trust.
Admit you lied, apologies, explain why you did it, and ask her that you hope she can forgive you. Then see how things go for a few weeks. You have seriously damaged her ability to trust you, and you'll have to earn that back.
Dump him and never take him back. If he lied to you once, he'll do it again. TRUST ME.
get a new boyfriend...
He had made the lack of trust worse when he lied.