The question is really asking which vegetation is the most likely to fall apart and shower emboli. Picture the building material of each. In infective endocarditis a clump of fibrin and platelets grows around colonies of living bacteria, most aggressively with Staphylococcus aureus. Because microbes keep digesting the surrounding tissue, these masses are bulky, soft, and poorly anchored, so chunks break free readily and lodge in distant organs. That softness is the definition of friability. Compare this to rheumatic heart disease, where the vegetations are tiny firm verrucae lined up neatly along the valve closure line and stuck down tightly, so they almost never embolize. Libman-Sacks endocarditis, which is simply the heart lesion of systemic lupus, throws up small sterile deposits on both faces of the valve cusps; being sterile and organised they lack the crumbly quality of an infected mass. Note also that the SLE option and the Libman-Sacks option point to the same disease, so neither can outrank infection. The clear winner for friability is infective endocarditis.
\[\boxed{\text{Infective endocarditis}}\]