Optical manipulation is interfacing disciplines in the micro and nanoscale, from molecular biology to quantum computation. Versatile solutions for increasingly more sophisticated technological applications require multiple traps with which to maneuver dynamically several particles in three dimensions. The axial direction is usually overlooked due to difficulties in observing particles away from an objective-lens focal plane, a normal element in optical tweezers, and in managing interparticle distances along the trapping beam propagating direction, where strong radiation pressure and shadowing effects compromise the simultaneous and stable confinement of the particles. Here, aperiodic kinoform diffractive lens based on the m-Bonacci sequence are proposed as a new trapping strategy. This lens provides split first-order diffractive foci whose separation depends on the generalized m-golden ratio. We show the extended manipulation capabilities of a laser tweezers system generated by these lens, in which concomitant trapping of particles in different focal planes takes place. Positioning particles in the axial direction with computer-controlled distances allows dynamic three-dimensional all-optical lattices, useful in a variety of microscale and nanoscale applications.