It's a huge thing to decide to end a relationship, especially when you have a child together, there are a lot of fears about money, arranging contact with the child and Dad in the future, your future, being alone etc.
When I was seeking advice on my old thread, under another name, I got some very wise advice, one person said to me "I know you want a stable father figure for your child, but it is equally important that your child see's their mother being treated with love and respect, both by a partner and by herself.
The message we send to our children when we sell ourselves short, by accepting far far less than we should, can have a profound impact in how they see themselves as adults and their expectations from relationships.
You do your children no favours by perpetuating a situation in which their father figure is unreliable and dishonest. Of course he will always be this person, but it may only be the end of your relationship that prompts him to reexamine this.
At the least, they will understand that their mother values herself too highly to be treated poorly, and this is a far greater example to set for them."
They were wise words, hard to swallow at the time and I didn't want to end things, but I look back now and I am thankful for the advice and they were right. It took me months to build up the courage to end it for good though and realise what the mumsnetters had said, was completely right 
I know on mn we often say leave the bastard, I try to not do that, perhaps my past really is colouring my pov on this thread, as I've said already, but I think you would be far far better off without a compulsive liar. There are good, decent, honourable men out there, you deserve one x