If the take-up lever on your Featherweight has been snapped off or its chrome is corroded the lever mechanism needs to be replaced. The machine will not sew with a broken take-up lever and if the chrome is corroded it may snag the thread.
Replacing the take up lever is not simple but neither is it very difficult. It involves removing two screws.
First remove the face plate.
The two screws to remove are the two larger ones you can see in the above photograph (not the tiny one at the top of the photograph) . The larger one is in a fixed position and the smaller screw moves as the take-up lever moves up and down.
Use screwdrivers that are the appropriate size for the slots in the screw heads slots.
The screws can be difficult to remove as they have been in place for 60+ years and probably have dried up oil "gluing" the threads in place.
The larger screw has normal threads and to remove it you turn it to the left. There is a washer that is between the lever and the body of the machine.
The smaller screw has a thread that is opposite to normal thread. To remove it you MUST turn it to the RIGHT. If you have trouble turning it to the right it is because the screw is stuck tight not because you are turning it the wrong way.
If you cannot remove the smaller bolt you cannot remove the take-up lever. You may have to resort to a hammer drill.
Both screws are removed in the above photograph.
Now you have to turn the hand wheel so the the take-up lever is in a position where you can wiggle the take-up lever and remove it.
You should have the four parts below.
Clean all the parts and the places on the machine from where the part was attached.
To install the replacement take-up lever do the reverse of the removal. As you are replacing the lever oil the parts as you proceed.
Install the small screw part first. Don't forget that to install the small screw turn the screw to the LEFT.
For the big screw the flat washer is under the lever against the body of the machine.