Luxembourg-Ville used precancels from December 1900 to 1925. The typographed precancels, introduced in 1908, show only the word "LUXEMBOURG" and the last two digits of the year of their validity. Many collectors and dealers mistake them for overprints or surcharges.
They were primarily used to send newspapers or printed matter, so uses on a cover such as you see here are scarce, even though many Luxembourg precancels, as loose stamps, are common.
This beautifully preserved mourning cover is franked with Luxembourg's 2c Coat of Arms definitive (Prifix No. 105) precanceled "16" for “1916” to pay the 2c domestic rate for printed matter up to 50 grams. While Prifix values the precancel off cover at only 25c, this cover realized € 163.00+ in an October 2012 European auction.
Precanceled mourning covers are uncommon, and especially so from Luxembourg, where precancel use was never extensive and was limited to just one town.
The standard reference on Luxembourg precancels is Dieter Basien, Handbuch zur Philatelie in Luxemburg, Lieferung 5.0, Vorausentwertungen (FSPL: 2005). An earlier work is Dr. A. Van Visschel, Die Vorausentwertungen von Luxemburg (Bund Deutscher Philatelisten e.V.: 1991).