Lorica Musculata made of Metal or leather?

[Dan Howard]

Well, maybe for parade purposes, but it completely negates the point of chainmail, which is flexibility.

That is precisely why it was worn in medieval Europe. The hardened leather acts as a ballistic shell to reduce the blunt trauma on the mail underneath. By the 13th-14th century, coats of plates and padded jacks were used instead.

FWIW the earliest mention of "cuirbouilli" in any text is the Chanson d'Antioche, which was written in 1180 but it describes events that occurred in the first crusade, so this type of armour could conceiveably be pushed back to the 11th century. There are no textual sources and no archaeological sources to suggest that it was used any earlier than this in Western Europe.