You launch something, usually a vehicle, when you start it moving. For example you might launch a boat or a rocket. You can also launch a project, for example "today is the big launch of our new campaign".
You lay something down when you place it into a resting position. You lay yourself down before you go to sleep. The picture is of someone laying a brick.
You laze around when you are idle and are doing nothing. The cat in the picture is lazing in the sun.
You lead someone or something when you take them somewhere. People usually lead animals by holding one end of a rope that is tied to the animal. The opposite of lead is follow.
Leap is another word for jump, particularly a big jump. The woman in the picture is leaping up into the air.
You lick things by wiping your tongue on them. Children usually lick lollypops or icecream and dogs lick people's faces.
You lift something when you raise it higher than it was before. The crane in the picture is lifting a heavy load. Lift is also another word for elevator.