It is shown that the contribution of the three-spin non-secular dipolar interactions of nuclei to their spin–lattice relaxation in solids can be measured with the modified conventional coherent pulse NMR technique at the laboratory-frame (LF) high frequency. In this method, the measurements are carried out in the specific magic-angle triply rotating frame (TRF), while the first (single) rotating frame (RF) is in the usual resonant coherent conditions and the second (doubly rotating) frame is in the conditions of the standard magic-angle. The procedure is similar to the well-known technique of measuring spin–lattice relaxation in the usual resonant RF. It is realized in the form of continuous spin-locking in the TRF effective field. The NMR signal is then registered in the form of the LF free induction decay (FID) after a sudden turn-off of a special-designed locking high-frequency pulse. The spin–lattice relaxation curve in the TRF is measured point-by-point by multiple repetitions of the experiment with varying the pulse length and recording the FID amplitude. Formulas for the contribution of the three-spin non-secular dipolar interactions into the TRF spin–lattice relaxation rate have been derived and quantitatively analyzed.