Concept:
Cell organelles may be membrane-bound or non-membrane-bound depending upon whether they are surrounded by a lipid membrane.
Understanding this distinction is important in cell biology.
Step 1: Examine Ribosomes.
Ribosomes are composed of rRNA and proteins.
They are not enclosed by any membrane.
Therefore ribosomes are non-membrane-bound organelles.
Step 2: Examine Vacuoles.
Vacuoles are enclosed by a membrane called tonoplast.
Hence they are membrane-bound structures.
Step 3: Examine Centrioles.
Centrioles are cylindrical microtubular structures.
They are not surrounded by membranes.
Therefore they are non-membrane-bound organelles.
Step 4: Examine Lysosomes.
Lysosomes possess a single membrane enclosing hydrolytic enzymes.
Hence they are membrane-bound organelles.
Step 5: Final conclusion.
The non-membrane-bound organelles are:
\[
I \text{ and } III
\]
Therefore option (D) is correct.