From the Wikipedia article on the place-name:
"The exact origin of the word is still a matter of speculation. 12th century AD author Geoffrey of Monmouth offered a fanciful etymology in his Historia Regum Britanniae, deriving the names of Cambria, Loegria, and Albany from the sons of the fictional Brutus of Troy: Camber, Locrinus, and Albanactus, respectively, and makes them the eponymous kings of Wales/Cambria (Camber), England/Loegria (Locrinus), and Scotland/Albany (Albanactus). In 1982, noted linguist Eric Hamp suggested that Lloeg(y)r could be derived from a Proto-Celtic compound *(p)les-okri-s, meaning 'having a nearby border, being from near the border'. Ranko Matasović prefers to see Lloegr as coming from a Brittonic collective noun *Lāikor meaning "Warriors", the root of which he proposes gave Old Irish láech "warrior" (though some scholars regard the Old Irish word as a loan from Latin laicus, "laity", "of the people"), from a Proto-Indo-European root *leh2- "war". The suffix -wys found in numerous Welsh folk names, including Lloegrwys, is derived from the Latin suffix -ēnsēs.
It seems to me we can simplify this considerably. Why not see Lloeg(y)r as merely a straight-across borrowing from the Latin genitive plural laicorum (m.)/laicarum (f.)/laicorum (n.), from laicus, “of or belonging to the people or laity, not priestly, not consecrated”? As is typical of Latin words that go over into Welsh, the -um suffix would be dropped, leaving "laicor."
If this name were used for England, it is probably a tacit acknowledgment that at least until the Saxons took over the country was still predominantly Romanized. A lay person was a Christian who had not been trained or ordained as a priest. But he could be clearly distinguished from a pagan.
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