Step 1: Recall essential amino acids.
Essential amino acids cannot be synthesized in sufficient quantities by the human body, so they must be obtained from the diet. The main essential amino acids are: Histidine, Isoleucine, Leucine, Lysine, Methionine, Phenylalanine, Threonine, Tryptophan, and Valine.
Step 2: Analyze each option.
- L-Phenylalanine: An essential amino acid needed for tyrosine and neurotransmitter synthesis.
- L-Valine: A branched-chain essential amino acid required for muscle metabolism.
- L-Lysine: An essential amino acid important for protein and collagen synthesis.
- L-Arginine: Considered a conditionally essential amino acid. It can be synthesized by the body in adults, but is essential for children and during stress conditions.
Step 3: Conclude.
Since the question asks for the one that is not strictly essential, the correct answer is L-Arginine.
Final Answer:
\[
\boxed{\text{L-Arginine}}
\]