Is it normal to sense when people are lying?

If anything, it's a very good trait. Most people would be able to pick up on things like this but since most people are pretty unobservant. This just means that you are much more observant than most, so you can pick up on signs that indicate that someone is lying. Since most people can't, they think it's weird that someone could notice things like this. Not everyone is able to, but some people can train themselves to or are just naturally observant without realizing it, like you.

you most likely just pick up on things intuitively more than most, i.e body language, involuntary facial movements, tone of voice, wording ect

perhaps you are also a good listener, which can help you find inconsistency's in the lie

there's no sure way to tell someone is lying, but most people will act in ways that will give it away.

its especially easy to tell if someone lying if you spend alot of time with them, as you are used to their usual way of acting and talking..

Most of us realize when we are being lied to but then there are times when the person is a good liar and pulls it off. There are signs that will help you read people. Read about body language. it's a good thing to know.

I'm pretty sure it's normal. i can have that to sometimes.

Sometimes people can sense things that others can't.

I mean there could be other reasons but i'm pretty sure it's just that you can sense things that some can't.

About all these doubts, there is no hard and fast rule to the best of my knowledge and belief.

It is for you to know your real potential powers, worth and value. Don't yield to others tactical methods or pressures, hypnotism or mesmerizing, etc. De-hypnotize them. It is not for them to judge. You are your own best judge.