You are describing the conversion of a massive lepton (an electron) into something, presumably not a lepton (a photon?), traveling at the speed of light. Either there is no conservation of lepton number, or a massive particle is traveling at the speed of light. In either case, we are no longer talking about classical physics.
The instance of mass/energy conversion (two-way process) is described by Mills in Chap. 28 of his book. He uses only classical laws of Newton, Maxwell, Planck, De Broglie and Lorentz. Two super-posed photons of opposite spin and energy of 511k eV strike a third body. A spherical resonator cavity of radius alpha * Bohr radius in free space (call the Transition State Orbitsphere) is created. As a resonator cavity, it has a characteristic frequency such that the two photons will experience infinite impedance and therefore "freeze" from E&M fields traveling a light speed into charge. Two particles are formed, a positively charged positron and a negatively charged electron, also as two orbitspheres. There's a lot more, including how this process results in the creation of gravity as space-time contracts. But, yes, it's all from classical physics.