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One of the Rangers who had been killed was the Lone Ranger's brother, Tonto made a mask from his shirt for the Ranger to wear until they caught the gang (so that he wouldn't be recognised by Cavendish). After they caught the gang the ranger decided to keep wearing the mask until the West was free of crime. So, that is why the Lone Ranger wore a mask.
I was in the supermarket last night and I saw a DVD with the first four episodes of the Lone Ranger on it, from 1949. As there was an opportunity to answer my own question about why the Lone Ranger wore a mask I bought the DVD and watched it when I got home. The Lone Ranger was one of a group of Texas Rangers tracking Butch Cavendish and his gang. The gang ambushed the Rangers and killed all but one of them (the Lone Ranger).