Step 1: Recall the two patterns of splenic amyloidosis.
Amyloid deposits in the spleen in one of two patterns, and pathology gives each a separate name based on where the deposits sit.
Step 2: Describe sago spleen.
When amyloid deposits are limited to the splenic follicles, that is the white pulp, the follicles look like firm, glassy granules scattered through the spleen, resembling grains of sago, so this pattern is called sago spleen.
Step 3: Describe lardaceous spleen.
When amyloid instead deposits along the walls of the splenic sinusoids and the surrounding connective tissue framework in the red pulp, the deposits can fuse together into large sheets. The cut surface of the spleen then looks pale, waxy, and firm like cured pork fat, which is called lard, giving this pattern the name lardaceous spleen.
Step 4: Match the pattern to the option.
Since lardaceous spleen comes from amyloid in the sinusoids of the red pulp, and not the white pulp follicles, penicillary arteries, or the trabeculae, the correct site is the sinusoids of the red pulp.
Step 5: Final answer.
Lardaceous spleen results from amyloid deposition in the sinusoids of the red pulp.
\[ \boxed{\text{Sinusoids of red pulp}} \]