I"d try to clean the points first and see whether that helps. I have an LA and some times they get a bit of greasy dirt on them after sitting around.
I pull a small strip of cardboard through a few times to remove the grease. Then a piece of wet/dry paper 400 grit a few times either side up. Followed by another piece of clean card again. They seem to be a pretty rugged well built magneto. There is a good book on magneto repair by Neil Yerigan. Doesn"t cover the same model Case magneto but similar. Depends on how far you want to go. Often a good clean is enough and go easy on the oil...