Kendrick Lamar simply slapped his lyrics on a Bill Withers song in order to crank out his track, "I Do This" ... but the costly problem is he did it without permission ... according to a new lawsuit.

Kendrick's being sued by Mattie Music Group, a music company that says it owns the rights to Bill Withers' song "Don't You Want To Stay," which was released back in 1975. 

According to legal docs filed by MMG ... the company says K. Dot's 2009 track "I Do This" is a complete replica of "Don't You Want To Stay" -- to the point it "consists of nothing more than new rap and hip hop lyrics set to the existing music of "Don't You Want To Stay."

Mattie Music is suing for damages and wants Kendrick to stop using the Withers track.