The integration of heterogeneous optical components onto an optical platform is crucial for the advancement of photonic chips. To achieve this, efficient coupling of optical signals between components and the platform is essential. Here, we have successfully integrated a Nd:YAG microdisk laser with a lithium-niobate-on-insulator (LNOI) photonic platform by modulating the propagation modes of LNOI. Ridge waveguides are fabricated on the LNOI by carefully adjusting the cross-sectional dimensions to enable the propagation of higher-order propagation modes. This ridge waveguide ensures that the effective refractive index of the higher-order mode closely matches that of the fundamental mode of the Nd:YAG microdisk, ensuring efficient waveguide-microdisk coupling. This on-chip laser, consisting of an Nd:YAG microdisk and LNOI integration, achieves a maximum output power of 23 µW, and a mode suppression ratio of 53.6 dB. This research presents an efficient approach for constructing highly functional heterogeneous integrated optical chips.