A lozenge is a kind of medicated candy that soothes your sore throat. If you've got a dry cough, you should drink some water and try sucking on a lozenge.
You might call a lozenge a "cough drop" or "pastille." Some have ingredients that ease the scratchy throat that causes coughing, and others are meant to relieve the discomfort of a sore throat. The word lozenge can also refer to a diamond shape. The tile on your bathroom floor might be a pattern of blue and white lozenges. Throat lozenges were originally diamond-shaped, hence the name.