The structural stacking order plays an important role for the magnetic ground state of atomically thin CrI₃. While bulk crystals undergo a transition from Monoclinic structure at room temperature to Rhombohedral structure at low temperature, bilayer CrI₃ maintains a monoclinic structure for all temperatures. Despite several studies, the absence of a structural transition in bilayer CrI₃ remains to be understood. Here we report on the study of bilayer CrI₃ on different substrates, using Raman and magneto-optical Kerr effect measurements to reveal the interplay between epitaxial strain, lattice structure, and spin ordering. We find that the lattice mismatch and resulting strain between the substrate and the CrI₃ flakes has a dramatic impact on the structure of the atomically thin CrI₃.