We interrogate 2 processes:
#(i)# #Li(g) + Delta_1 rarr Li^(+)(g) + e^(-)#
#(ii)# #Li^(+)(g) + Delta_2 rarr Li^(2+)(g) + e^(-)#
Now just from an electrostatic point of view, we would anticipate that #Delta_2>Delta_1# simply on the basis that it should be harder to remove an electron from a positively charged species, #Li^(+)#, to make a dication, #Li^(2+)#, than from the neutral metal atom to make a cation. Why? Because the electron is more tightly bound to a formal cation.
So, as physical scientists, let us put in some numbers:
This site reports that for lithium, #Delta_1=520.2*kJ*mol^-1#, and #Delta_2=7298.1*kJ*mol^-1#.
So in fact our facile expectation was correct. However, the substantial magnitude of #Delta_2#, which dwarfs #Delta_1#, also reflects the electronic stucuture of the lithium atom. The second ionization requires the removal of a #1s^2# electron, rather than than a #2s^1#, which was the one first removed. Because this second electron is inner shell, its attraction to the nucleus should be quite substantial, and our data support this expectation.
