We report the first demonstration of broadband adiabatic directional couplers in thin-film lithium niobate on insulator (LNOI) waveguides. A three LN-waveguide configuration with each waveguide having a ridge cross section of less than 1 square micron, built atop a layer of SiO2 based on a 500-µm-thick Si substrate, has been designed and constructed to optically emulate a three-state stimulated Raman adiabatic passage system, with which a unique counterintuitive adiabatic light transfer phenomenon in a high coupling efficiency of >97% (corresponding to a >15 dB splitting ratio) spanning telecom S, C, and L bands for both TE and TM polarization modes has been observed for a 2-mm long coupler length. An even broader operating bandwidth of >800 nm of the device can be found from the simulation fitting of the experimental data. The footprint of the realized LNOI adiabatic coupler has been reduced by >99% compared to its bulk counterparts. Such an ultra-compact, broadband LNOI adiabatic coupler can be further used to implement or integrate with various photonic elements, a potential building block for realizing large-scale integrated photonic (quantum) circuits in LN.