Hint: As we know lithium and sodium both are alkali metal and lie in group $1$ in periodic table. Sodium and lithium donate an electron to attain a noble gas configuration. Therefore they are univalent electropositive metals
Complete answer: Sodium react with water more vigorously than lithium because by the following reasons; Sodium is greater than lithium in size because as we go down the group size of alkali metal increases due to an extra shell. As the size of alkali metal increases their ionization enthalpy decreases as a result their reactivity increases toward water because as ionization enthalpy decreases alkali metal can donate its electron more easily. Hence sodium is greater in size than lithium it reacts with water more vigorously than lithium because it is more electropositive metal because of low ionization enthalpy. As we go down the group electropositive character increases due to decrease of ionization enthalpy. Therefore we can say that sodium reacts with water more vigorously than lithium because it is more electropositive metal.
So the correct option is $C.$
Note: It is to be noted that the size of lithium is too small so it cannot donate an electron to form a univalent cation because the small size force of attraction between electrons and protons is too much greater as compared to other alkali metals. As we know the size of lithium is smaller than other alkali metals so it cannot form ionic compounds more easily. Therefore it forms covalent compounds whereas other alkali metals form ionic compounds.