It all depends what they lied about and why. Some people lie due to embarrassment or shame. Though, if someone straight up lies for no good reason...then yes, I tend to lose respect and trust in them.
Of course! If I trusted someone and learned they had lied to me, they would not be the respectable person I thought they were. That person never existed and, therefore, I would not have any respect for the newly-revealed liar at all.
It depends on the lie. If it's like an exaggeration to make oneself appear a little better than they are, then I can understand. I don't do this myself, but we all have insecurities we try to mask, keeping them from being revealed. that's only human. I think it would be a over the top to call that a "betrayal of trust". What I don't find acceptable is flat out deception, at the expense of my trust.
Its a basic fact of the human condition that everyone lies the only differential is what they lie about. Depending on what type of lie (most people tell the middle to the worst) I would say a definite yes.
I lie all the time. Sometimes I do it for fun especially on the internet. I'm a mother of three (truth). I will lie through my back teeth to protect them. The loss of random peoples respect makes no dent. The loss of theirs would be devastating. I never lie to my kids and I never betray them. Everybodies respect isn't necessary. Pick those you care about and endeavour to always behave in a way towatds them that instills trust. That is all.