We report a muon spin rotation ($mu^{+}$SR) study of the magnetic properties of the double perovskite compound LaSrNiReO$_{6}$. Using the unique length and time scales of the $mu^{+}$SR technique, we successfully clarify the magnetic ground state of LaSrNiReO$_{6}$, which was previously deemed as a spin glass state. Instead, our $mu^{+}$SR results point towards a long-range dynamically ordered ground state below $T_{rm C}= 23$ K, for which a static limit is foreseen at $T=0$. Furthermore, between 23 K$<Tleq$300 K, three different magnetic phases are identified: a dense ($23$ K$<Tleq75$ K), a dilute ($75$ K$<Tleq250$ K), and a paramagnetic ($T>250$ K) state. Our results reveal how two separate, yet intertwined magnetic lattices interact within the unique double perovskite structure and the importance of using complementary experimental techniques to obtain a complete understanding of the microscopic magnetic properties of complex materials.