Step 1: Separate the two lens deformities. Lenticonus is a conical protrusion of the lens, and its direction (anterior versus posterior) is tied to specific syndromes.
Step 2: Anterior lenticonus is the hallmark of Alport's syndrome. The posterior variety is linked with Lowe's syndrome, the oculocerebrorenal disorder.
Step 3: The two remaining options describe dislocated rather than cone-shaped lenses. Marfan syndrome typically shows upward lens subluxation and homocystinuria shows downward subluxation, so neither is lenticonus.
Step 4: The oil-globule appearance in the red reflex confirms lenticonus, and in the posterior form the cause is Lowe's syndrome.
\[\boxed{\text{Lowe's syndrome}}\]