early 14c., "plane figure having four equal sides and two acute and two obtuse angles," from Old French losenge "rhombus shape, diamond-shape" (as an ornamental motif in heraldry, etc.); "small square cake; windowpane," etc., a word used for many flat quadrilateral things (Modern French losange). It has cognates in Spanish losange, Catalan llosange, Italian lozanga, but the origin is disputed.
Probably from a pre-Roman Celtic language, perhaps Iberian *lausa or Gaulish *lausa "flat stone" (compare Provençal lausa, Spanish losa, Catalan llosa, Portuguese lousa "slab, tombstone"). From late 14c. as "diamond-shaped cake or wafer;" specific sense "small cake or tablet (originally diamond-shaped) of medicine and sugar, etc., meant to be held in the mouth and dissolved" is from 1520s.
The related words in Continental languages often have a sense "flattery, deceit" (compare Old French losengier "to praise unduly," losenge "flattery, false praise; deceitful friendliness"), which comes probably via the notion of square flat slabs of tombstones and their fulsome epithets. Some of this made its way into Middle English via French. Chaucer uses losenger "flatterer, deceiver;" losengerye "flattery."