"Lugs" is the nickname for the relationship between Bugs and Lola.
Canon Episodes/Merrie Melodies That Feature "Lugs"
Bugs first meets Lola in the episode, "Members Only", where they met on the tennis court and instantly fell in love. It only took one date, before noticed she was crazy. Lola broke up with him, to date Pepe Le Pew.
In "Eligible Bachelors" Lola dumps Pepe and bids 100,000 dollars on Bugs for the bachelor auction.
After that, they have been dating ever since, and it was revealed in "Double Date" that Bugs may still have feelings for Lola.
We Are in Love
Lola and Bugs also sing a Merrie Melody, "We Are in Love."