Caught in a lie

So, backstory: Me and this guy have been talking for a little over three months. He lives in Australia, I live in the US. Things are getting serious, and we've already made plans to go to Colorado for an entire month in December. Well over the past 2 months, he seems to get upset when I hang out with friends. I ask him what the problem is and he says nothing is wrong but still acts like it. We were fighting A LOT for a few weeks, and things just started to get better. We were starting to get closer. Last night my friends wanted me to go out. The party didn't start until 11:00. Me and my boy were talking on the phone until 12:30. I didn't tell him I was going out, I just told him I was going to sleep. I lied because I didn't want to start a fight with him, and I didn't want him to accuse me of going because of a guy or getting super drunk. I just wanted to hang out with my girl friends without having a fight. And I was only there for an hour. I got in the car with my friends to leave the party, and I meant to send a Snapchat to someone but accidentally sent it to my boy (yes that's what I deserve, and karma came back to bite me). I wasn't dancing with other guys, I didn't even talk to another guy. I literally lied so he wouldn't worry about it and to save us from a fight. It honestly was not because I wanted to get drunk and grind on guys.

I know that the lie itself is wrong, and uncalled for. I should have told him no matter how mad he would of gotten. Just one time I wanted to go out without fighting. I didn't want to keep from him that I was going out, but I knew I wasn't going out for another guy and it wasn't to get shitfaced. My reasoning for going out was truly innocent, but he still would have said that I was wanting attention from other guys if I had told him.

Now he has caught me in the lie, and of course he doesn't believe me. He has every right not to believe me. I just want to know how I can make this better? What's the best way to gain someone's trust back?