Tempini was a Steel producer in Brescia, already well known for its Glisenti revolvers etc, well before WW I.
This 37mm case would indicate that Tempini drew the case (Brass) and probably also forged the Projectile;
Loading (“filling”) would have been done at a separate ( “Servizio d’ Artiglieria” or Naval “Arsenale”) location, or even exported.
The stamping “Lorenz Brevettato” indicates the case/shell design was a Lorenz MunitionsFabrik (Part of DWM) Patent design.
This would have applied in normal practice before Italy entered WWI ( ie, 24th May, 1915)…all Foreign ( ie, Enemy) Patent royalties would have been paid to a “Trust” holding Enemy Alien
Businesses and Properties until disposition at the end of the War.
The “MF” could be either an Inspector’s Mark, or a Filling Factory mark; in any case, it is of different type style from the Tempini-applied Factory ID. The Date stamp is also in a “serif Style” and applied either on completion of the shell case, or at its assembly. If MF is an Inspector’s Mark, it would follow the Italian convention of Surname first, first name last. The other Possibility is the Naval Dockyards and Arsenal of Monfalcone, near Venice.
It may be that the shell was “work in progress” in early 1915, and was taken over by the Regio Marina, which used Hotchkisses on TPDs ( Torpedo Boat Destroyer…Destroyers to us, "Caccia Torpediniere
I had a 25 mm shell with the same Lorenz headstamp, but different government (?) marks