In the days before car ignition systems had ballast resistors, a lot of cars wouldn't actually fire while the starter was running. They would only start when the battery voltage recovered as the starter was turned off, but the engine was still turning fast enough.
Technique was all important here, because you had to crank it for a short time and then release the starter button when the engine was going fast enough to fire. The more recent technique of operating the starter and letting go when you heard the engine fire simply didn't work. If you tried that, the battery would soon be flattened and the cranking rate would slow, and the battery would not recover fast enough when you let go of the starter.
If you're not wanting lots of people to drive the car, it might be quite simple to try a different starting technique. It's certainly a cheap solution.
However, if the Lingenfelter module has been designed sufficiently badly not to work at around 6 V, it might take some time to start working when the battery voltage recovers and so the engine will have stopped before the the module works.
I learned to drive in my mother's 1953 MG (YB model). It never started until I let go of the starter button. However, I could use the crank handle if needed.
As an example of how much technique matters, quite a few years ago I was helping a work colleague get his Honda going. The ignition switch was excessively complicated and had a heater output so the sequence was:-
Off
Aux ...... Radio only on
Ign ....... Radio, heaters and ignition on
Start ..... Ignition and starter motor on
The idea was to save the battery by turning the heaters off during cranking. Unfortunately, cramming all of that into a small switch meant that it couldn't take the current and the ignition feed part of the switch burned out.
When I realised that, as a temporary measure until a new switch arrived, I disconnected the heater feed, and connected the ignition feed to the heater terminal on the switch, so the sequence became:-
Off
Aux ...... Radio only on
Ign ....... Radio, ignition on
Start ..... Starter motor on
So then the car would not start when the key was turned, but the starter would turn the engine, and when I let go, the ignition would come on and the engine would start.
Well I could start this car every time. The owner could never get it to start. He only had to turn the key and let go about 1 - 2 seconds later, but he was too used to turning the key and holding it there until he heard the engine fire. He got the car towed to a garage and a new switch fitted there.