Having to purge the line after the engine has sat for a while or after the hose is disconnected from the tank is normal. Air gets into the system. Once the engine has started you should be able to stop it and restart it all day long.
It should run fine on either a gas feed tank or liquid feed tank. It has a vaporizer in the system. In fact on a really cold day a gas feed tank might not supply enough propane to give you full power from the engine. I run my 15 on a forklift liquid feed tank.
The starter sounds weak. Have you tested the voltage at the starter? I’m thinking voltage drop between the battery and the starter. That one uses an external battery doesn’t it? You could get them with a small battery under the engine cover.
What happens when you hand crank it?
I think I have a pdf of the service manual. If you will PM your email to me I’ll try to send it to you. Probably not much help without parts being available.
I have both the PDF and original paper manual I got with the engine. My version of the engine has an external battery, with no alternator. I run a solar panel, and controller, so it has enough voltage.
(A later version of the Lehr had an alternator, and small starter battery inside the cowl.)
If I purge the propane in my start procedure and turn the key, it will start 10 times in a row.
https://imgur.com/a/Jc5nOiZ
"Purge, Turn Key, Starts like in the second video."
"No Purge, Turn Key, Won't start, like in the first video."
"Purge, Turn Key, Start like in the second video."
I can go back and forth purge, no purge, and the results are consistent. The battery will start only after a purge. I have spent over half an hour going back and forth, because I've tried every shut down procedure I could think of, and tried to start it with out bleeding it.
It doesn't start, then I bleed it, start it, and try a new shut down procedure.
Bleeding it is the only thing that works!