Step 1: Examine the assertion.
MHC Class I molecules present endogenous (intracellular) peptides to
\[
\boxed{\text{CD8}^{+}\text{ cytotoxic T lymphocytes}.}
\]
Hence,
\[
\boxed{\text{Assertion [A] is true}.}
\]
Step 2: Examine the reason.
Endogenous peptides are generated mainly by
\[
\boxed{\text{Proteasomal degradation in the cytoplasm},}
\]
not in lysosomes.
Lysosomes generate peptides for the MHC Class II pathway.
Therefore,
\[
\boxed{\text{Reason [R] is false}.}
\]
Thus,
\[
\boxed{(C)}
\]
is the correct answer.