Lying is way too common and there are even people who have never told anything honest in their lives if they could avoid it. To some people it has become second nature. Not all lies are created equal though, for example someone could lie that they are ok when they are not ok at all,to avoid exposing their vulnurabilities. This is a defence mechanism to keep people out and avoid getting emotionally exposed and hurt. Then,you have the lies abusive people tell,and the most common reasons I have seen abusive people lie are pretty telling about their character.
An abusive person will lie subtly in front of other people,just enough to get what they want, but they won't hesitate to lie blatantly in their victim's face. Even when the truth is obvious and exposed, the abusive liar will stick to their story and act offended that they have been outed as liars.
Lying to impress people : though many people try to impress others by exaggerating their accomplishments or even adding a couple lies, an abuser will not just want to look cool in front of their friends. They are actually trying to convince everyone of their positive attributes or impress people so that when you come out and tell them that this person is abusive,no matter how much proof you have, no one will believe you because there will be tons of people swearing that your abuser is a great person.
Lying to take advantage of people : Abusers love using people for their own benefit. They usually just demand and order people around,but if all else fails they start lying until they get you to bend over backwards. They will lie that they forgot to run an errant but they are too tired now and can't do it even though it is really important,they will lie that they don't have time but there is a deadline,they will lie that they don't know how to do this, and so on and so forth,lying non stop until someone else does everything for them.
Lying to avoid consequences for their behavior : That's fairly obvious, I will not explain this one in detail but I will give some examples of the forms this type of lying might take. The abuser might pretend that their memory is unstable and then mention something trivial you did a long time ago that to them is proof that you are the bad guy. The first few times,the "unstable memory" act might convince you but it's obvious that their unstable memory only exists when they have to admit their wrongdoings and face the consequences of what they do. They will claim that you are lying, no matter how much proof you have. They will claim that you are accusing them of things that you did,not them. They will claim that MAAAAYBE part of what you accuse them of MIIIIGHT have happened, but it was not as bad as you said. When they finally make you back down on accusing them of their wrongdoings, they will gloat about what they did to you and how you deserved it so badly.See?They do remember it all,and it was actually bad,and it did happen,the abuser just lied to avoid all consequences and when they finally made you back down they revealed that you were right all along and gloat that you can't do anything about it anymore. This is a type of gashlighting, which is a terryfying type of mental abuse with long term damage. It can cause not just insecurities and fear,but a ton of mental issues that might even be permanent.
Dealing with an abusive liar is not that easy most of the times, you might find yourself just giving up and compromising to avoid conflict many times,but honestly it's not worth it,they are not worth it. Always keep in mind that the lying abuser is a lying abuser, when they blatantly lie or bend the truth for their own nefarious purposes,don't believe anything they say. When you know the truth about something and they lie in front of you to strangers who don't know,call them out. You can do that by bluntly stating the facts and exposing their lie -only do this if you are not too close to the liar and you won't be putting your self in danger. Or you can do that in a more subtle way,by correcting them and attributing their lies to memory failure,but then you are giving them the benefit of the doubt and people will just brush the lies off as an "honest" mistake and not suspect malicious behavior until they face it too. Though more subtle,this way of calling out a liar is less possible to get caught and put you in danger from the abusive liar lashing out while also alerting people that this certain person is not telling the entire truth.
Take care and remember,someone who lies to others with no shred of remorse just to take advantage of them, is not a person you want in your life.Someone who lies in the face of evidence to avoid even just apologising for a malicious behavior,is not someone you want in your life. No matter if it is your parent,sibling, friend or partner, you don't want to get involved with those people,instead keep in mind who they really are,remove them from your life and never contact them again. No matter what the relation is,you are better off without them in your life.