I'd suggest doing a little measuring. First of all total length of screw. Then the thread size. Then the ID of the hole in the arm.

Find a screw long enough with the right threads. Find a bushing that fits inside the hole and over the screw. Find a washer that will keep the lever arm from sliding off. Purchase and install.

There were two barrel carbs made up through the 1970s that used a similar screw.

But you can fake one quite easily.

R.