High pressure Raman and angle dispersive X-ray diffraction (ADXRD) measurements on the metallic hexaboride LaB₆ have been carried out upto the pressures of about 20 GPa. The subtle phase transition around 10 GPa indicated in Raman measurements is confirmed by ADXRD experiments to be a structural change from cubic to orthorhombic phase. Ab-initio electronic band structure calculations using full potential linear augmented plane wave method carried out as a function of pressure show that this transition is driven by the interception of Fermi level by electronic band minimum around the transition pressure.