Lady Gaga -- Attacks Songwriter Who Sued Her ... with a Vengeance

Call Lady Gaga a thief ... and then prepare to cough up more than a mil to pay her army of lawyers who will tear you apart in court.

Gaga has filed court docs -- obtained by TMZ -- to collect nearly $1.4 million she paid her lawyers ... to fight a woman who sued Lady G for allegedly ripping off one of her songs.

Gaga -- one of the richest women in music -- claims she spent nearly three years and a fortune defending her reputation ... and in the end she won. A judge threw out the case ... concluding the 2 songs sounded nothing alike.