This work presents a reconfigurable opto-microfluidic coupling between optical waveguides and tilted microfluidic channels in monolithic lithium niobate crystal. The light path connecting two waveguide arrays located on opposite sides of a microfluidic channel depends on the refractive index between the liquid phase and the hosting crystal. As a result, the optical properties of the flowing fluid, which is pumped into the microfluidic channel on demand, can be exploited to control the light pathways inside the optofluidic device. Proof-of-concept applications are herein presented, including microfluidic optical waveguide switching, optical refractive index sensing, and wavelength demultiplexing.