Due to their excellent electro-optic, acousto-optic, and nonlinear optical properties, lithium niobate (LiNbO₃) materials are widely recognized as ideal platforms for developing high-performance integrated optoelectronic chips. In recent years, advancements in micro-nano processing technology and successful fabrication of wafer-scale lithium niobate on insulator (LNOI) thin films have led to substantial advantages in integrating large-scale high-speed optoelectronic device on the LNOI platform. With the successful realization of fundamental communication devices such as high-speed modulators that utilize optoelectronic integration technology, increased attention has been given to advanced multiplexing techniques that extend data capacity by transmitting multiple channels in parallel. In the LNOI platform, various integrated photonic devices based on multiple multiplexing dimensions have been developed with the aim of achieving monolithic integration of high-speed and large-capacity optoelectronic communication devices. This paper explores LNOI waveguides and recently reported multi-dimensional multiplexed LNOI integrated photonic devices, including key technologies such as optical signal multiplexing, manipulation, and control in wavelength, mode, and polarization dimensions. We also detail the working mechanisms, design principles, methods, and performance parameters of the devices. Finally, this paper discusses the current challenges and potential solutions for implementing multi-dimensional multiplexed integrated photonic devices in the LNOI platform.