The microring resonator based on lithium niobate on insulator (LNOI) is a promising platform for broadband nonlinearity process because of its strong second-order nonlinear coefficients, the capability of dispersion engineering, etc. It is important to control the energy transmitted into the resonator at different wavelengths, as this becomes difficult for two bands across an octave. In this Letter, we study the effect of different pulley bus-resonator configurations on phase mismatching and mode field overlap. We achieve the control of energy transmission coefficients at different wavebands simultaneously and provide a general design methodology for coupled structures for broadband applications. This paper can contribute to quantum and classical optical broadband applications based on LNOI microring resonators.