Lithium niobate on insulator (LNOI) platforms promise unique advantages in realizing high-speed, large-capacity, and large-scale photonic integrated circuits (PICs) by leveraging lithium niobate's attractive material properties, which include electro-optic and nonlinear optic properties, low material loss, and a wide transparency window. Optical mode interleavers can increase the functionality of future PICs in LNOI by enabling optical mode division multiplexing (MDM) systems, allowing variable mode assignment while maintaining high channel utilization and capacity. In this Letter, we experimentally demonstrate an optical mode interleaver based on an asymmetric Y-junction on the LNOI platform, which exhibits an insertion loss of below 0.46 dB and modal cross talk of below -13.0 dB over a wavelength range of 1500-1600 nm. The demonstrated mode interleaver will be an attractive circuit component in future high-speed and large-capacity PICs due to its simple structure, scalability, and capacity for efficient and flexible mode manipulation on the LNOI platform.