Based on the setup of the question, we do not need the melting point of lead because the question say the specific heat capacity of solid and molten lead are the same.
But what is lacking is the specific latent heat of fusion of lead.
If we attempt the question algebraically, we can see that the melting point of lead is eliminated in the solution.
m is the mass of lead
θ_L is the melting point of lead
θ_f is the final temp
Lf is the specific latent heat of fusion of lead
v is the speed of the bullet
c is the specific heat capacity of solid and molten lead
Thermal energy gains by the solid lead bullet = m × c × (θ_L - 40)
Thermal energy gains to melt the solid lead bullet = m × Lf
Thermal energy gains to raise the temperature of the molten lead = m × c × (θ_f - θ_L)
KE of the bullet = 0.5 × m × v^2
Using conservation of energy
Loss of KE = Gain of thermal energy