Michaelis-Menten constant ($K_m$) and enzyme substrate affinity:

• The Michaelis constant ($K_m$) is inversely related to the enzyme's binding affinity/specificity for the substrate (a lower $K_m$ indicates higher affinity). Given values: $K_m(E3) = 5 \times 10^{-15} \lt K_m(E1) = 5 \times 10^{-12} \lt K_m(E2) = 5 \times 10^{-10}$. Therefore, the order of specificity is $E3 \gt E1 \gt E2$.
• Statement (A) is correct because $K_m(E1) \lt K_m(E2)$, meaning E1 has higher affinity than E2.
• Statement (B) is incorrect because E2 has the highest $K_m$ and thus the lowest affinity.
• Statements (C) and (D) are correct because E3 has the lowest $K_m$, meaning it is more specific than both E1 and E2.

IUBMB Enzyme Commission classification:

• Lyases (EC 4) catalyze the cleavage of $C-C$, $C-O$, $C-N$, and other covalent bonds by elimination mechanisms (without hydrolysis or oxidation), leaving double bonds or rings, or conversely adding groups to double bonds.
• Oxidoreductases (EC 1) catalyze oxidation-reduction electron transfer reactions.
• Transferases (EC 2) transfer specific functional groups (e.g., methyl, glycosyl, phosphate) from one molecule to another.
• Isomerases (EC 5) catalyze geometric or structural rearrangements within a single molecule.