It doesn't sound very good to me.
Does he text other people that often and that late at night too? Not suggesting other women but other friends and family? And if so, are those texts also deleted?
If he's doing the same thing for lots of people it might not be as bad as it seems, although the previous lying is still a big worry. If it's just her, I would be worried.
I don't want to say too much about this as it happened to a friend of mine, but her husband did a similar thing. Lots of texts and phone calls to a girl (she was 18, he was much older) who had recently started to work with him and he talked about her a lot as just a friends as she had a fiancé.
When my friend got suspicious he protested a lot, refused to end his friendship and stop any contact with the girl, which he could have done as he was working in a different office by then and away from her.
My friend got all the blame for being paranoid and jealous and weird and spiteful and every other name he could call her. He said he had a right to have friends and a right to send messages without being questioned and that my friend was controlling and manipulative and he was just an innocent victim of her paranoia.
The girl and her friends were posting abuse about my friend on Facebook and the fiancé rang her to call her a liar.
My friend was pregnant at the time with their second child.
And just when she felt she was going mad and was as bad as he was making her out to be, the girl rang her up and confessed to having had sex with him. Turns out when he had had enough of her he ended things and she was spiteful enough then to tell the truth, which he finally admitted.
Actually I've said quite a lot there but sadly this is all to common