I have that marking on several early SMLEs. It seems to have fallen out of style during the Great War.
But it is definitely as detailed above.
Long rifles were marked "LEI" or "LEI*" and Carbines were marked "LECI".
Then they came up with the SHORT rifle, which was very much an innovation..... so they marked it clearly. Only in the rush of things did it get shortened yet again, to "SMLE".
If you ever asked a Great War veteran what type of rifle they carried, they would say, "Short Lee-Enfield": the "Short" was ALWAYS there.
Hope this helps.
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