Trust Issues

I'm going to try and explain this as quickly as I can:

So I have been in this relationship for just about a year now and he is incredibly happy with us and everything. I am too, it's just. He has a friend and she is very forward with him. She makes out that she doesn't like him in that way but she then starts sitting on his lap, resting her head on his shoulder. A while back they went out as mates and she was trying to hold his hand and was just acting very weird with him.
What concerned me was that he didn't tell me about any of this... he didn't even speak to her and tell her that she was being out of order. I was out with some friends one night and one of them got very drunk and tried to kiss me. I stopped him straight away and told my boyfriend and spoke to this friend the next day and told him he was out of line. It was only then that my boyfriend decided to tell me about his friend acting weird that time they went out, which had happened around a month prior to this.
After this, we had an argument because he had done some *****y things (nothing to do with anything I have mentioned) and I asked him if he had told anyone about it. He had told this girl and twisted the whole thing in order to get some form of sympathy out of her. He lied about it many times and when I asked to see the conversation he deleted a bunch of messages so that I wouldn't know what he said. He continued to lie but it finally came out and I saw the whole conversation.
Before he lied, I didn't mind too much what was going on. I kinda trusted that he was now going to tell me if anything weird happened with her and that he would talk to her about it. I wasn't 100% sure but it was enough to not let it bother me too much. Now, I have no trust in him after he lied to me so many times and I am just constantly stressing that something is happening and he won't tell me about it or lie about it in order to get out of trouble.
It has got to point where I just can't trust even small things he says and it is really getting in the way of our relationship which is really horrible because everything else is so perfect.

I guess what I want to know is:
-What do you suggest I do?
-Do you think you can gain back trust from someone you once lost it from?

Thank you.

I'm going to try and explain this as quickly as I can:

So I have been in this relationship for just about a year now and he is incredibly happy with us and everything. I am too, it's just. He has a friend and she is very forward with him. She makes out that she doesn't like him in that way but she then starts sitting on his lap, resting her head on his shoulder. A while back they went out as mates and she was trying to hold his hand and was just acting very weird with him.
What concerned me was that he didn't tell me about any of this... he didn't even speak to her and tell her that she was being out of order. I was out with some friends one night and one of them got very drunk and tried to kiss me. I stopped him straight away and told my boyfriend and spoke to this friend the next day and told him he was out of line. It was only then that my boyfriend decided to tell me about his friend acting weird that time they went out, which had happened around a month prior to this.
After this, we had an argument because he had done some *****y things (nothing to do with anything I have mentioned) and I asked him if he had told anyone about it. He had told this girl and twisted the whole thing in order to get some form of sympathy out of her. He lied about it many times and when I asked to see the conversation he deleted a bunch of messages so that I wouldn't know what he said. He continued to lie but it finally came out and I saw the whole conversation.
Before he lied, I didn't mind too much what was going on. I kinda trusted that he was now going to tell me if anything weird happened with her and that he would talk to her about it. I wasn't 100% sure but it was enough to not let it bother me too much. Now, I have no trust in him after he lied to me so many times and I am just constantly stressing that something is happening and he won't tell me about it or lie about it in order to get out of trouble.
It has got to point where I just can't trust even small things he says and it is really getting in the way of our relationship which is really horrible because everything else is so perfect.

I guess what I want to know is:
-What do you suggest I do?
-Do you think you can gain back trust from someone you once lost it from?

Thank you.