The lever drops the one box. You don't really need to move it to get the kittens home.
Take the lift up to the top crate,
dig under neath it so it falls
while granny is holding onto the rope move the crate one space
dig under neath it so it fall on the blue button that opens all the doors.
drop down and get the kitten and take it home using the lifts.
Use the lifts to get the bonus flowers.
when the exit flower appears go down the ladders to it.
granny can move the one crate to the blue button on the left by using the lifts.