The RW stands for Remington Works. The serial number does not start with an "L". If it's 133xxx it would be 1912. If it's 233xxx it would be 1913. 333xxx would be 1915. 433xxx would be 1918. 533xxx would be 1920. After that, there would be a date code on the left side of the barrel just ahead of the receiver. The home page has a box where you can enter barrel codes and find out the month and year of assembly. The RW stamping was dropped in September, 1924 so your rifle was made before then.
The complete chart of months and years is in Roy Marcot's & my book advertised under books on this site.