A

Step 1: Understand the concepts behind the energies associated with atomic systems. The binding energy of electrons in atoms can be found using the formula for ionization energies and the principles of quantum mechanics.

Step 2: Analyze each row in Column-I:
(i) **Binding Energy of Electron in Doubly Ionized Lithium Atom**: The binding energy can be approximated using the formula related to the hydrogen-like atom: \( E = 13.6 \cdot Z^2/n^2 \) where \( Z \) is the atomic number (3 for Li) and \( n \) is the principal quantum number. For Li²⁺, the electron is in n=1, so:
\[ E = 13.6 \cdot (3^2)/1^2 = 13.6 \cdot 9 = 122.4 \, ext{eV} \] which matches with [C].

(ii) **Energy required to remove electron from the first excited state of Triply Ionized Beryllium Atom**: For Be²⁺ in the first excited state (n=2):
\[ E = 13.6 \cdot (4)/2^2 = 13.6 \cdot 1 = 13.6 ext{ eV} (Ground state) \] therefore it should be much less, typically = 3.4 eV which matches with [B].

(iii) **Ionization energy of tetra ionized boron**: For B³⁺, again using the formula for binding energy:
\[ E = 13.6 \cdot (5^2)/1^2 = 13.6 * 25 = 340 ext{ eV} \] matches [A].

(iv) **Assembling singly ionized helium atom**: For He⁺:
\[ E = 13.6 * (2^2)/1^2 = 54.4 ext{ eV} \] matches with [D].

Conclusion: The correct matches are:
(i) [C], (ii) [B], (iii) [A], (iv) [D].
Thus, the appropriate option is A.