My exH was a liar. Often about quite little things. If pulled up on those, he'd either deny lying, or just say, 'Well, it could have been like that'. He called that 'the imaginative truth'.
It was odd/funny/quirky at first, when these were all small matters - embellishing the truth about things that had happened. Later it became so tiring, so exasperating, as he began to lie about bigger things. Though, to be fair, he never lied about being in trouble with the police (as far as I know).
This was a fair few years ago, so no mobile phones. But you'd be amazed at how many times the train he was coming home on was cancelled or delayed! i.e. he was unable to get in touch with me when we'd made arrangements to do something (a bit like your OH and his phone being out of charge).
He was also an alcoholic, so some (many) of his lies were to cover up the time and money he spent down the pub. This may not be the case with your OH, of course.
We didn't have children, which made it easier for me to leave in the end. But it took me several years. I loved him, but I just couldn't live like that.
And it wasn't just me he lied to - the stories I heard from his friends and his family (even people he was really fond of)! He just couldn't help himself.
He was unhappy with himself, frustrated at the fact that what he wanted to be did not match the reality of what he was doing with his life. We both knew that, but he said he couldn't (wouldn't) do anything about it. I guess he was afraid. I tried to help him; I couldn't. He needed to help himself; I'm so sorry for him that he was unable to do that.
Offred has given you some excellent advice here.
I wish you the best of luck 