Lennie is carrying the dead mouse because he likes to touch soft things. He loves soft, furry animals and dreams one day of living in his own farmhouse with George and raising rabbits.
Unfortunately, he is mentally challenged, and sometimes doesn't realize his own strength. Often, when he is petting small animals, he is too rough. He accidentally killed the mouse by squeezing it too hard. Now he is afraid to tell George because he is afraid he will be angry and not let him help with the rabbits someday. He is still keeping the mouse, though, because it is soft, and he likes to feel it in his hands.
The mouse is also symbolic. Enotes analysis page states that the crushed mouse is a foreshasowing of the frailty of the men's dreams and the inevitable way they, too, will be crushed.
Lennie carries the dead mouse because he likes to touch soft things and he knows George will take it away from him if he sees it.
it was aforeshadow....later lenny kills curleys wife becuase her hair was soft and the rat's hair was soft
lennie could pet it with his thumb while they walked along
he likes to touch soft things
like later in the book with the girl in the red silky dress in weed, he touches it and she accuses him of rape
and after that when he gets his puppy he pets it to hard and breaks his neck
and in the end when he touches curly's wifes soft curly hair and kills her