The noun lancet describes a small, double-edged surgical knife used to make incisions.
A lancer is a soldier bearing a long spear, called a lance, while a lancet is like a tiny spear — sharp on two sides and meant to pierce things. And though a soldier could wield a lancet, it's more likely to be used by a surgeon. A lancet arch is an architectural term used to describe an arch that peaks at the top. Most buildings with lancet arches are not places where you’d use a lancet, though.