Is there some psychological term or words that describes someone who is not telling the truth? Then, what would you also call a situation or psychological term / words where someone tries to cover something up and ends up making more mistakes by trying to cover up the numerous lies?

The term pathological liar comes to mind.

"Oh, the tangled web we weave."

Why do you want to know the linguistic terms?

Currently involved in a situation where someone has routinely not told the truth, in fact perjury is even involved. So, trying to find politically correct name to refer to this type of individual.

Compulsive liar
In denial would be the 'polite' PC term.