Step 1: Analyze Statement I.
Saturated fatty acids do not possess double bonds.
Hence false.
Step 2: Analyze Statement II.
Lecithin is a phospholipid.
True.
Step 3: Analyze Statement III.
Glycerol is trihydroxy propane.
True.
Step 4: Analyze Statements IV and V.
Palmitic acid contains 16 carbons, not 20.
False.
Arachidonic acid contains 20 carbons, not 16.
False.
Therefore only II and III are correct.
\[
\boxed{\text{Option (C)}}
\]