The incorrect statement is

We need to identify the incorrect statement about first ionization enthalpies.

Option A: The first ionization enthalpy of K is less than that of Na and Li

In Group 1 (alkali metals), ionization enthalpy decreases down the group: Li > Na > K. So the ionization enthalpy of K is indeed less than both Na and Li. This statement is correct.

Option B: Xe does not have the lowest first ionization enthalpy in its group

In Group 18 (noble gases), the ionization enthalpy generally decreases down the group, but Radon (Rn) is below Xe and has a lower ionization enthalpy. However, due to relativistic effects and the stability of the filled shells, the trend holds that Rn has the lowest. So Xe does NOT have the lowest ionization enthalpy in Group 18. This statement is correct.

Option C: The first ionization enthalpy of element with atomic number 37 is lower than that of element with atomic number 38

Element 37 is Rubidium (Rb, Group 1) and element 38 is Strontium (Sr, Group 2). As we move from Rb to Sr, the nuclear charge increases and the electron is being removed from the same shell. Group 2 elements generally have higher ionization enthalpy than Group 1 elements in the same period. So IE of Rb < IE of Sr. This statement is correct.

Option D: The first ionization enthalpy of Ga is higher than that of the d-block element with atomic number 30

Element with atomic number 30 is Zinc (Zn). Gallium (Ga, Z = 31) has a lower ionization enthalpy than Zinc. This is because Zn has a completely filled $$3d^{10}4s^2$$ configuration which is extra stable, and its ionization enthalpy (906 kJ/mol) is higher than that of Ga (579 kJ/mol). So Ga does NOT have higher ionization enthalpy than Zn.

This statement is incorrect.

The correct answer is Option D.