I need the wiring diagram for the Lakewood heater QTV-22

SOURCE: Cycles on and off after reaching desired temperature

The problem sounds like the thermostat which is probably a bimetal strip. It sounds like the bimetal strip is just constantly bending one direction then the other. It could be possibly adjusted by bending it -- this would be a trial and error process.

Or, it could be replaced.

SOURCE: ROCKER SWITCH DIAGRAM

On the top of the switch (inside the heater) there is a common connection.....even though it looks as if it is connected (electrically), it isn't electrically affected by the switch; it's just used as a post. It's just the place where the striped wire connects to the "common" point for the heater coils (they are in a parallel). Also, while you're in there you might want to put some electrical grease on the exposed conductors.....mine had quite a bit of corrosion (which was the reason for the failure). I had to replace 3 of the female connectors.

SOURCE: I have a Lakewood QTV-22 750/1500 Watt heater and one of the tubes doesn't heat up when I turned it on. Is it safe to use?

yes
as the elements are in parallel
have an appliance shop replace the faulty element