Is mentioning the trait of lying, which is prevalent in a person and causes embarrassment to friends, considered backbiting? And how can this backbiting be expiated if it has occurred?

All praise is due to Allah.

Backbiting has been forbidden by Allah in the Quran and Sunnah (definition), and this prohibition includes both the obedient and the disobedient. It is permissible to mention shortcomings if there is a legitimate, recognized Sharia (definition) benefit, such as advising people or warning against someone who openly commits sins. However, mentioning a friend's shortcomings is considered forbidden backbiting, even if that characteristic is present in them. Your prayer for their guidance does not absolve you of the sin of backbiting. What is obligatory for one who has backbitten is to repent to Allah.