Answer : 220.65pm,91.35pm
The cubical closest packing has a face-centred cubic unit cell.$I^-$ ions occupy the corners and the face centres.These ions touch each other along the face diagonal of the cube.Hence
$4r_{I^-}=\sqrt 2 a$
$r_{I^-}=\large\frac{a}{2\sqrt 2}=\frac{624pm}{2(1.414)}=$$220.65$pm
Now along the edge,we will have $I^-Li^+I^-$ arrangement,where $I^-$ are at the corners and $Li^+$ ion at the centre of the edge (octahedral void ).Since in closest packing,they touch each other,we will have
$2r_I^-+2r_{Li^+}=a$
$r_{Li^+}=\large\frac{a}{2}$$-r_{I^-}=\large\frac{624pm}{2}$$-220.65pm=91.35pm$