**Core Concept**
The question is testing the ability to identify a fungal infection in an immunocompromised patient, specifically an HIV-infected individual. The presence of yeast-like morphology on a Gram stain of lung aspirate suggests a fungal etiology.

**Why the Correct Answer is Right**
The most likely diagnosis is Pneumocystis jirovecii pneumonia (PCP), a common opportunistic infection in HIV-infected individuals. PCP is caused by the fungus Pneumocystis jirovecii, which is a dimorphic fungus that exhibits yeast-like morphology in its trophic form. The fungus typically infects the lungs and can cause severe pneumonia in immunocompromised patients.

**Why Each Wrong Option is Incorrect**
**Option A:** Histoplasmosis is a fungal infection caused by Histoplasma capsulatum, which is also dimorphic and exhibits yeast-like morphology. However, it is not the most likely diagnosis in an HIV-infected individual with lung aspirate showing yeast-like morphology.
**Option B:** Coccidioidomycosis is a fungal infection caused by Coccidioides immitis, which is a dimorphic fungus that exhibits spherule morphology, not yeast-like morphology. Therefore, it is not the correct diagnosis in this case.
**Option C:** Aspergillosis is a fungal infection caused by Aspergillus species, which are typically hyphal in morphology, not yeast-like. Therefore, it is not the correct diagnosis in this case.

**Clinical Pearl / High-Yield Fact**
In HIV-infected individuals, Pneumocystis jirovecii pneumonia (PCP) is a common opportunistic infection that can be prevented with trimethoprim-sulfamethoxazole prophylaxis. PCP is often referred to as an "AIDS-defining illness" because it is a hallmark of advanced HIV disease.

**Correct Answer:** C.