My husband once lied about badminton. He allowed me to win then said he had not let me win! I did find out, and I went on and on about it for years! I hate when people lie.
But I know I am guilty of embellishing the truth myself.
I have no idea if these are red flags or not!
I would not be happy with a partner talking about our sex life and that would be the thing that would probably bother me most after lying. But, again, I have mentioned one or two things about my sex life to a friend myself!! And I can see that he might well deny saying it when caught out.
Personally, I would not see him embellishing a story a bit as a huge issue, as long as he is not putting other people down in the process, e.g. if it's a 'you won't believe the size of the fish I caught' kind of story!
The lie today about the picture, well I find that the least bothersome. Maybe he didn't actively show it to his fiend, maybe his friend looked over his shoulder or grabbed his phone.
For me the issue is that you sent him a photo and he thought he knew you would be annoyed if he showed it to someone else, and then did (disrespectful of him) or over reaction (on your part)?
It's up to you but if you are going to continue in your relationship I think I would have a talk (in your shoes) about why lying is so destructive in a relationship. That you want the truth, because lies are corrosive, and really eat away at a relationship. I would also, personally, call him out in private about any exaggerations etc.
It kind of sounds like you are a bit out of synchronisation with each other. He has told a friend about your sex life, maybe thinking you would disapprove and lied because he thought you would disapprove but actually you wouldn't disprove of him telling. is that right?
He has shown a photo, or allowed a friend to see it, (not exactly the same thing) a photo of you and again, thought you would disprove, and you would not have!
You said I had considered asking him why he lied the other day about the incident to friends but part of me didnt want to give him the heads up that i had noticed his lying so that if he did it to me he wouldnt be so conscious of hiding it if that makes sense? I guess that tells me i knew he would.
Are you wanting to catch him out or stop him lying? If to catch him out, then don't give a heads up, but if you want to educate him about wjat you think is not OK then you will need to tell him.
Maybe you need to make it clear what in your mind is and is not OK and, of course, LYING for you will be big on the list. Knowing that LYING is big on the list if he keeps on doing it, then I would consider if this relationship is worth it. But do remember that exaggeration is not exactly the same as lying and if you include that you probably need to stress that to him.