so, I've been trying to get my head around boundaries and found this statement “If you (behavior), I’ll share my feelings with you. If you continue, I’ll (action) to take care of myself.”
Firstly, I don't like the sentence "I’ll share my feelings with you", it sounds wishy washy and I don't understand it's purpose; what could it be replaced with?
Secondly, how would I apply this specifically to when I've caught him lying to me again?
I took the boundary sentence you quoted and applied it more to my own internal thought processes ... .
So applying it to your situation, I might say this to myself:
Jeez, he's sometime seeing this other woman. I feel blechy about this. I don't like it one bit. Is he with her now? I've resorted to spying on him, checking through his phone then calling him out on it. He lies about it. This situation leaves me feeling out of control. How can I regain control of my emotions?
By being aware of your boundaries! Your values. What matters most to you

Then being able to share all of this with him in a non-confrontational way
I hope it doesn't come down to this for you, but I had to be willing to leave the relationship for there to be any kind of serious change. I had finally had enough and knew I had to get my mojo back, with or without him in my life

I spoke honestly from my heart. MY heart, that I wasn't happy with this arrangement. That what I want in life matters and I'm going for it. I'd love for him to be a part of it. I'll also be fine on my own... . And I meant it. I still mean it. I've detached from some of the silly stuff, some of the moods and oddball things he says and does once in a while... . The heart of our relationship is pure. I accept that he has a disorder. I accept him.
Are you really okay with him seeing this other woman? It's okay if you aren't. It's okay if you are. It's up to you to figure all of that out. If you're staying with him, knowing that he does this sort of thing, telling him that you can understand why he does it-- Does it make sense to check up on him then get mad when he lies about it?
Is it really the lies that you're upset about?