High-rate Neutron Depth Profiling (NDP) is a very efficient and precise probe for studying the evolution of lithium concentration in thin-layer structures, e.g., battery electrodes. NDP is typically limited to a one-dimensional depth analysis summed over the profile area covered by the neutron beam. We developed a detector system based on double-sided silicon strip detectors (DSSSD) with extremely thin and homogeneous entrance windows to provide a new quality of NDP measurements in 3+1 dimensions for the N4DP instrument at the FRM II in Garching, Germany. Using the ⁶Li(n, α)³H reaction in an experiment conducted at the research reactor in Delft, we achieved a lateral position resolution down to ∼100μm and an energy resolution with FWHM≈10keV for the triton particles at energies of 2.7MeV. High-resolution 3D pictures with a contrast uncertainty <10% per pixel can be achieved faster than 1 picture per minute. This rate can be adjusted individually for each experiment by sacrificing granularity in the position measurement.