The radii of the lithium and magnesium ions are 76 pm and 72 pm, respectively. which compound has stronger ionic attraction, lithium oxide or magnesium oxide

 From the Born–Landé equation the lattice energy U ∝ (Z+ × Z-) / (r+ + r-) where Z+ and Z- are the charges on the cation and anion, respectively; r+ and r- are radii of the cation and anion, respectively.

The Z+×Z- term dominates. MgO has 2×2 (4) so it will have the higher U than Li2O Z+ × Z- = 2.
You only consider (r+ + r-) term when the Z+×Z- term is the same; smallest the (r+ + r-),  the larger is the U. 
U(MgO) = 3795 kJ mol^-1
U(Li2O) = 2799 kJ mol^-1 

MgO has larger.