All door handles have screws that secure the outer and inner handle together. The lever style door handle is no different. Some lever handles, like rotary handles, have screws that are hidden behind the inner faceplate rather than screwing through the faceplate. Removing a lever style door handle that appears to have no screws requires removing the inner door handle to access the screws.
Open the door halfway so you have access to both door handles. Locate a small hole on the inside lever stem. The hole is often under the bend of the lever handle near the door lever faceplate on the door.
Insert a small nail or a straightened large paper clip into the hole. The resistance that you encounter is the spring mechanism that locks the lever onto the handle stem. Press in on the spring with the paper clip or nail.
Pull the inner door lever away from the door while pressing on the spring with the paper clip. With your fingers, twist the lever faceplate off the mounting plate on the door. The screws securing the inside mounting plate and the outer door lever mechanism are now visible.
Remove the screws on the inside mounting plate with a Phillips screwdriver. These screws go into sleeves on the outer door handle mechanism as well as the mounting plate.
Lift the outer door lever mechanism out of the door, and pull the inner mounting plate away from the door. Remove the screws securing the latch assembly to the edge of the door with the screwdriver, and remove the latch assembly.