"LITHGOW" on the barrel?
And it's a Metford?
What else do the markings on the barrel say?
The best I have been able to establish is that Lithgow made Lee ENFIELD barrels as replacements for private and governments users that required them, up until the time that the AustralianRifle Club /Association rules changed in the early 1930's as I recall, so that "range rifles" more or less had to conform to "Service" spec, i.e., 25.2 inches, not with 30.2 inch barrels. There are still a lot of "abbreviated" LE "Range Pattern rifles floating about. Interestingly, they shot surprisingly well, and, in the spirit of "gamesmanship", SMLE shooters wanted a "fatter / stiffer" barrel, just like the profile of the lopped LE barrel. Hence the Lithgow "H" barrel, later to turn up in the "H T" Service sniper rigs. I've seen some odd stuff over the years, but never a Lithgow-made replacement Metford barrel. I'm getting used to surprises after all these years, however.
Unless it is utterly smoothbored / shot out, you should be able to count the rifling grooves: Five for an Enfield, seven "polygonal grooves" for a Metford. Even near-mint Metfords look like they are "shot out" to the untrained eye that is expecting nice, clearly-defined rifling grooves. See also H&K G3 . HK91 barrels.