We report a calculation of the ground state binding energies of the on- and off-axis neutral, D0, and negatively charged, D−, donors in an oblate lens-shaped InAlAs/GaAlAs quantum dot in the presence of a uniform magnetic field applied parallel to the dot axis. The calculations have been performed by using the adiabatic approximation for the electron, a Bastard-type trial function for the D0, and the Hylleraas-type trial function for the D− ion. Novel curves and contour plots for the energies of donors confined in a quantum lens as functions of the distance from the axis for several dot heights and magnetic field strengths are presented. We show that under strong magnetic field the on-axis D− ion binding energy becomes larger than the corresponding value of the D0 located in the peripheral region close to the barrier, making possible the formation of on-axis D− centres in equilibrium via electron transfer from the peripheral donor to the on-axis D0.