Sadly, if your behaviour continues he will leave. I kept lying and disappointing my girlfriend of two years and she recently moved out. All I can do now is work on myself, for myself and get better. Will we get together again, I don't know, but right now I don't have her here and it looks like she will never be back. It's not too late for you though, you've already taken the first step and you should be proud of that. Just find out why you lie, are you afraid or do you do it to make yourself look better? Look deep inside yourself, think back to how you think when you've lied. Let your partner know why you do it and how you plan to stop it.
One thing you could do is tell your boyfriend that if you lie, he can give you 24 hours to own up to it, that way when you've lied your brain will know you have 24 hours to own up and believe me the guilt will force you to be truthful. In time you'll get better, as I said this is the first step and you should be proud of that.

Start small... everything counts..
Do it for yourself first ur man will notice it...
Just like any addiction we must work on it...
Am not liar but my man is... m here because i googled how to help loved one who lies...

But m food addict... i work on it
I journal days i dont eat sugar n i exercise.... no one noticed in the beginning but later whole world can see results...

But i knw my weakness ... wen my heartbreaks i go bk to sugar ...

Similarly work on ur lie...
Also helps if u know ur weakness... so that u can forgive urself and get up to be a stronger person...

Hope this helps

The two things that helped me the most right at the beginning was to figure out who I was, look in the mirror look at yourself figure out who and what you really are. Then decide who you want to be. A truthful person and honest person and whatever other goals you might have we are life comma and make a detailed plan to get to that point. Follow that plan every day. Every day.