Lead is solid at its melting point. then they begin to melt it. How does the internal energy of lead change in this case?

The internal energy of a substance is the sum of the kinetic and potential energy of all their molecules that the substance consists of.

The internal energy of a body depends on the temperature and state of aggregation of matter.

Since the temperature of a substance in a liquid and a solid state at the melting point is the same, the internal energy will be determined by the state of aggregation of the substance.

To transfer a substance, at the melting point, from a solid state to a liquid, it is necessary to expend an amount of heat. The internal energy in the liquid state will be greater than in the solid state by λ * m.

λ is the specific heat of fusion, m is the mass of the substance.