Is "I'm lying" a paradox?

This is the famous "Liar's Paradox", let's analyze it:

A paradox means that there are two opposite conclusions in the same proposition, and both conclusions can be self-justifying.

That is: event P can deduce event not-P; event not-P can deduce event P

The proposition "I am lying":

If it is true words, then "I am lying" itself is a lie and contradicts the truth.

If it is a lie. Then "I am lying" is a lie, which is contradictory to falsehood.