Answer: Infective endocarditis.
Step 1: A vegetation is a friable mass of platelets, fibrin, microorganisms and inflammatory cells that sits on a heart valve. The classic large, destructive, organism-laden vegetation is that of infective endocarditis.
Step 2: All four options can produce valvular lesions, but the term vegetation most strongly and specifically denotes infective endocarditis, where microcolonies of bacteria are embedded in the fibrin-platelet mass.
Step 3: Contrast the others. Libman-Sacks (SLE) gives small sterile verrucae on both surfaces of the valve. NBTE (marantic) gives small sterile vegetations along the line of closure in debilitated or hypercoagulable patients. Rheumatic fever gives tiny verrucous vegetations along the valve closure line plus chronic scarring. These are smaller and sterile, so infective endocarditis is the best single answer.
Ref: Robbins and Cotran Pathologic Basis of Disease, 10e.