The metallic lustre exhibited is caused by:
Oscillation of loose electrons
Low ionization energy of Sodium
Excitation of free protons
Existence of body centered cubic lattice
When light falls on the surface of sodium, the free electron starts oscillating at its mean position and get excited to higher levels. On returning back to lower levels, it emits light in all directions. Due to this sodium has a characteristic metallic lustre.
Hence, the metallic lustre exhibited by sodium is explained by oscillation of loose electron.