We carried out a systematic theoretical study on how spin affects the phononic properties of CrI3 monolayers. We find that the frequencies of two infrared-active (IR) modes are significantly influenced by the magnetic configuration. Thus an IR spectrum may be applied to identify the magnetic order by utilizing the spin-lattice correlation. The thermal expansion coefficients are 2.21, 3.35 and -5.58 × 10-6 K-1 for ferromagnetic (FM), antiferromagnetic (AFM) and paramagnetic (PM) phases at 30 K, because of the competition between the modes with negative and positive Grüneisen constants. Furthermore, the lattice thermal conductivity is also sensitive to the magnetic phase, which is attributed to the spin-dependent lattice anharmonicity. Our results provide fundamental insights into the spin-lattice coupling and clarify the potential of a spintronic monolayer as a thermal switching device for active heat flow control.