I would recommend expressing to her that you're not able to continue contact for the time being and if she isn't willing to keep trying you'll need space from her to sort your feelings. You can set a time frame for no contact and step back to focus on yourself, and if she refuses to respect your space you may need to block her temporarily.

If she's unwilling to continue trying, there isn't much you can do. You cannot force her to stay with you just because you believe you can change and "fix" things. Focus on yourself for a while; figure out what drove you to cheat and lie and work on healing from the cause so you never hurt a partner in that way again. Move on and take care of yourself.