Should I end relationship even though I love him

Stay only if you can live with a pathological liar.

Or a habitual liar, or just a liar.

You love him but do you like him?

He really doesn't sound very likable. He continues to lie to you and cover up his actions. Don't you deserve to be treated better?

You place yourself in a conundrum when you state that rationally, you should end it with him, because you can't trust him, yet emotionally, you say you still love him.
I don't see a good choice that YOU can make here, because whichever you choose, you will always feel: did I make the right call?

My suggestion is that you do a, what do you call it, temporary break-up? Basically, just say that you need time and space to think about this relationship, and suggest he give you that space, by moving out(or you moving out, whichever suits you better). Mind you, it's just temporary. The way I see it,
a) You'll get a chance to seriously consider the pro's and cons of this relationship, without him around, clouding it for you emotionally at least.
b) He'll get to show how sincere he is in wanting to chance of better himself: if anything, this step shows him that you are in a serious quandary about this relationship, and that puts the ball in his court: either he mans up and meets your demands, or he doesn't, and give you an extra reason to end this.

That's just my two cents: whatever you opt for, I wish you the best of luck!

His kind if behavior does not change. It’s a compulsion - done even when there are consequences.