Step 1: Analyze the statement.
Lucky (male) said that the person in the portrait is the "only child of my paternal grandmother's daughter."
The "paternal grandmother's daughter" is Lucky's mother.
The "only child of my mother" would be Lucky himself, but since the statement refers to a different person, it implies that the person in the portrait is Lucky's cousin.
Step 2: Conclusion.
Thus, the portrait that Lucky is looking at is his cousin.
The correct answer is:
\[
\boxed{{His cousin}}.
\]