I would tend to think that the locomotive was probably also used for construction trains.
There were three parallel routes that the company had between the Los Angeles suburbs and Redondo. One was the original alignment converted, the second was built at the time of the conversion to electric and 42", and then a third one was built. The Los Angeles Railway also had an agreement to use the inner portions of these lines for local streetcar service. In 1911 the inner portions went to the streetcar company and the outer portions to Redondo were converted to standard gauge and connected to a cross country line the ("new") Pacific Electric built from Watts to El Segundo. 1910-11 is when the interurban lines in the Los Angeles are were combined into the "new" Pacific Electric which was owned by the Southern Pacific. The Los Angeles Railway got all of the PE and LA&R trackage used for 42" city-type service. LARy was owned by Henry E. Huntington.
The 42" gauge 4-4-0 was listed as sold to a gravel operation following the 1911 merger.
Brian Norden