Properties of the stability diagram and exchange energy of a few-electron laterally coupled quantum dots in magnetic fields are investigated. The calculations are performed by numerically exact diagonalization of the many-body Schrödinger equation. We show variations of the energy separation between the single-particle ground and first excited states, and the exchange energy with biases on the two dots at different magnetic fields. Two-dimensional single-particle wavefunction and electron density profiles show electron localization with magnetic fields. From the extracted double-triple point separation on the stability diagram, we also show that the coupling strength decrease as the magnetic field increases.