The aluminum on those handles are soft. I use handles exactly like that one. I have the single on the left..clutch, and double pull on the right for brakes. I keep the aluminum adjustors screwed all the way in and adjust the cables on the other ends....at the clutch arm and at both brakes. Doing it this way you'll never have a problem with the lever screw adjustors. This may not be the answer you're looking for but it prevents the little, soft aluminum adjustors from screwing up.
There are better quality cable pull handles but mostly won't be found on Ebay or Amazon. They are sold at bike shops and the prices will probably send most back looking on Ebay or Amazon.
The handles we have are sufficient for the job and the price is good. You just have to handle them in certain ways for it to last.
If you are determined to use the lever adjustor on those handles it is probably wise to take the screw adjustor off, make sure all threads are clean, carefully close the screw ring closed to where its fairly tight on the barrel thread , and keep it lubricated to prevent the aluminum from shredding tiny pieces between the threads. Then use it sparingly if you want it to last.
The aluminum adjustor is the same on button or 3 position lever locks.
Edit..
I had searched a while back and didn't use the right search terms. There's a bunch on Ebay that are priced in the range suitable for our use but I did not see lever locks on these sets.
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