Does any one know old German 22 long rifle single shot with a marking on top of breach that says mod 1 and a logo in the stock that is a small L linked to a large S who made this gun and how old is it?

There are books published that list the manufacturer's logos and identify the manufacturers. Find a copy of "Gun Marks" or look for copies of 1970's Gun Digests, which also had articles on different nationalities gun marks.