Step 1: Identify the syndrome. Prolonged fever (3 weeks), splenomegaly, a hypoechoic splenic lesion (suggesting a splenic abscess), and crucially a Gram-negative bacillus on blood culture.
Step 2: The blood culture result is the discriminator. The organism must be a Gram-negative bacillus that grows on routine blood culture.
Step 3: Among the options, only Salmonella (typically Salmonella typhi causing enteric fever) is a Gram-negative bacillus. Enteric fever classically gives prolonged fever and splenomegaly, and the spleen is the commonest visceral site for a typhoid abscess.
Step 4: The other options do not fit. Cytomegalovirus and the Epstein-Barr type lymphoma-associated virus are viruses, not Gram-negative bacilli. Toxoplasma is a protozoan parasite. None would be reported as a Gram-negative bacillus on a bacterial blood culture.
Step 5: The clinical picture of enteric fever with a splenic abscess and a Gram-negative bacillus on culture points to Salmonella.
Answer: C. Salmonella.