A phrase used in a small regional cluster in the northeast US. It means to ensure that your own needs are met without regard to what others may want or need. Can be used in the first person, second person, or third person, such as “my piece of lasagna, your piece of lasagna, or his/her piece of lasagna.”
“My piece of Lasagna” - Everybody at the ballgame wanted a beer, but Jenny just got up and went to the concession stand and came back with only one. When her thirsty friends protested bitterly, she responded - “I don’t care if you all are hot and thirsty. I got MY piece of lasagna!”