If someone has cheated and lied but claims they have made bad choices and has learned from them can you trust the person?
Trusting anybody is a personal choice. You need to know what the consequences will be if you allow that person to dissapoint you ever or again. If you are willing to give the person a second chance do that with a forgiving heart. But do be careful not to make this your life patern
I cannot think of any excuse, reason, or explanation, that makes cheating acceptable. In order to forgive and move forward, I have to accept living with a lying cheater. I could never do that.
I believe the only reasons someone would stay with a lying cheater, are not good reasons, so the "relationship" cannot ever be one of trust and respect.