I need thoughts and opinions

I have lied to my girlfriend about something terrible. I recently confessed to it and to all the lies that led up to it. I had been talking to my ex girlfriend who I only see as a friend and only have ever seen as a friend after our breakup. My ex and I haven't dated in 3 years and my ex is with someone else as I am as well. Early in the relationship with my girlfriend and I, we were browsing on social media and she saw a picture of my ex and I. She questioned me about who it was and I told her it was a friend. It was beyond stupid of me to lie about that. I lied because I didn't think she wouldn't understand why we still talked. It does seem crazy to be friends with an ex, but my ex was there for me as a friend only. Months later, before I confessed to my girlfriend about still being friends with and talking my ex, I had told her she was a best friend in my phone. I told her she was another best friend from home in fact. (Even more stupid) I dug my hole deeper. To make matters worse I had my ex portray messages as to being the other friend, that was my "best friend from home". Before I lied again and made matters even more worse I confessed to my girlfriend about everything. I completely betrayed my girlfriend and lied several times about talking to my ex. I never lied about anything else in our whole relationship especially to lie about something so stupid and not worth it was the dumbest decision I've ever made in my life. I told my ex to stop contact with me again and that our friendship was over. I have apologized and owned up to every lie I told my girlfriend about this situation with my ex. It was completely wrong and I should've told her from the beginning. I should of never tried to stay friends with my ex during our relationship. It wasn't worth all the hurt I caused her and myself for being dishonest and betraying her like that. I have to earn her trust, respect, love all over again to make this work and I to be forgiven by her. I know I'll have to work really hard for her forgiveness and trust again. I love her and I shouldn't of lied to her about something so stupid. I think she is beyond worth trying to mend this. I know it'll take time to mend things and for us to heal from this. Should I continue this relationship? Should I try to make it work even knowing it's not going to be easy? Thoughts and opinions would be greatly appreciated.