In his mind when he lies to you he is "protecting" you.
No offense, but a person with NPD would never think this, or care to protect another. He also wouldn't cry as reality set in, and telling him over and over that you love him is only begging to be crushed by such a person.
I'm certain, Ladya, that your H has some very serious issues, but these are just not the actions of a person with NPD.
NPD people are very cold underneath their charming exterior. Their entire world revolves around hiding the real 'them' and instead using others to validate themselves. They are not 'conceited' as is often mistakenly thought. They are in fact extremely insecure under all of the bluff they display. They read people, extremely well, and generally when a person meets a NPD for the first time, they think the NPD is just the nicest, most charming person ever!! (oh, if they only knew). This is because the NPD has no 'real self' and only mirrors others to behave in ways to get the validation from others that they need.
Once an NPD views a person as 'weak' as would be the case for someone that has been cheated on and instead of being angry simply reminds the narc how much they love them, they discard them. It's termed 'devalue and discard'. It is what sends most over the edge with a NPD. They try desperately to get back to that honeymoon stage, and in doing so the NPD views them as lesser, and begins to be cruel and uncaring. The reality is they were always uncaring, they just hid it.
You cannot reason with NPD. You cannot 'love' them to you. You cannot win them over, and you cannot get 'on the inside' with them. They simply are not wired like the rest of society. However, unlike a true Sociopath (or antisocial), the NPD is not born this way. This is a situation created during the very early years of a person's life. It is believed that by the time a person is 4 or 5, NPD has taken hold, if it is going to.
There are a couple of different causes for this, but the end result is the same. There is no empathy, no concern, no genuine care underneath the facade of an NPD person. There is only the desire for validation and admiration (supply), and a brutal cruel streak if they suspect they are going to get anything less.
If you find yourself with an NPD, the only real option is to end the relationship. There is no real relationship with an NPD, so the only thing being left is the fantasy that this 'person' genuinely cares for you, or anyone.
Again, all cheaters display NPD traits. It comes with the territory. But a true narcissist? It's very unlikely.