Landau-Zener (LZ) tunneling, i.e., the nonadiabatic level transition under strong parameter driving, is a fundamental concept in modern quantum mechanics. With the advent of non-Hermitian physics, research interest has been paid to the LZ tunneling involving level dissipations. However, experimental demonstrations of such an interesting non-Hermitian LZ problem remain yet elusive. Here, by harnessing a synthetic temporal lattice using a fiber-loop circuit, we report on the first real-time measurement of non-Hermitian LZ tunneling in a dissipative two-band lattice model. An innovative approach based on mode interference is developed to measure the transient band occupancies, providing a powerful tool to explore the non-Hermitian LZ tunneling dynamics in non-orthogonal eigenmodes. We find that the loss does not change the final LZ tunneling probability but can highly affect the tunneling process by modifying the typical band occupancies oscillation behaviors. Our work initiates exploring intriguing LZ physics and measurements beyond standard Hermitian paradigm, with potential applications in coherent quantum control and quantum technologies.