I would like to know how to do the following problem (would you use the Born-Haber cycle?)

the value of the second ionization energy for Ca, 1145 kJ/mol, calculate the lattice energy of CaF2.

you need to use Born Haber's cycle

Ca(s) --->  Ca(g ) (Sublimation enthalpy in  KJ per mole )
Ca(g)---.>Ca+1(g )  +1e(first ionization energy in KJ/mol)
Ca+1(g )  ----> Ca+2(g )  +1e(second ionization energy in K J/mol)
F2 (g) ------>2F (g) (Bond enthalpy in KJ /mol)
2F + 2e------>2 F-1(g) (2x electron affinity in KJ/mol)
  Ca+2(g )+ 2 F-1(g) ----> CaF2(s) ( lattice energy in KJ/mol)
to get the desired equation
Ca(s) + F2(g) ---> CaF2(s)
add all the enthalpies with proper signs
Try it now