A FUCKING LIAR!

so I’m trying to build trust from him lying so much to me and him cheating and I really want this to work but he lied to me again and even tho it was the smallest lie he argued with me to try and cover it and I got it out of him anyway!!! Idk what to do should I leave him or teach him a lesson or what??? I love him and I really wish and want him to change!!!!