Refer to:
http://www2.ucdsb.on.ca/tiss/stretton/database/Standard_Reduction_Potentials.htm
Ba²⁺(aq) + 2e⁻ → Ba(s) E° = -2.90 V
Pb²⁺(aq) + 2e⁻ → Pb(s) E° = -0.13 V
Ba(s) + Pb²⁺(aq) → Ba²⁺(aq) + Pb(s) E°cell
E°cell = E°(red) - E°(oxid) = [(-0.13) - (2.90)] V = 2.77 V
As E°cell = 2.77 V > 0, the reaction is spontaneous.