**Core Concept**
Lattice formation is a phenomenon observed in the interaction between antibodies and antigens, leading to the formation of a visible lattice or network. This process is crucial in various diagnostic tests, such as the latex agglutination test, where the presence of specific antibodies is indicated by the formation of visible lattice structures.

**Why the Correct Answer is Right**
The correct answer choice, C, indicates that lattice formation is indeed associated with both precipitation and agglutination. In precipitation reactions, the antibodies and antigens interact to form a visible precipitate, which is essentially a type of lattice structure. Similarly, in agglutination reactions, the lattice formation leads to the visible clumping of particles, such as bacteria or red blood cells, when specific antibodies bind to their surface antigens. The lattice formation is facilitated by the cross-linking of antibodies and antigens, resulting in the visible aggregation of particles.

**Why Each Wrong Option is Incorrect**
**Option A:** This choice is incorrect because lattice formation is indeed associated with precipitation, not just precipitation and not agglutination. Precipitation reactions involve the formation of a visible precipitate, which is a type of lattice structure.

**Option B:** This choice is incorrect because lattice formation is also associated with agglutination, not just agglutination and not precipitation. Agglutination reactions involve the visible clumping of particles, which is a result of lattice formation.

**Option D:** This choice is incorrect because lattice formation is indeed associated with both precipitation and agglutination, not neither.

**Clinical Pearl / High-Yield Fact**
A key point to remember is that lattice formation is a critical aspect of various diagnostic tests, including the latex agglutination test, where the presence of specific antibodies is indicated by the formation of visible lattice structures. Understanding the principles of lattice formation is essential for interpreting the results of these tests accurately.

**✓ Correct Answer: C. Associated with both**