In this article, we propose a robust control strategy using direct Lyapunov strategy (DLS) for a single-input dual-output three-level dc-dc converter (SIDO-TLC) while the output loads and voltage references are disturbed. The first proceeding is to concurrently focus on the current and voltage dynamics of the converter buck and boost segments for exerting the related variable errors to the DLS-based function. Accordingly, through a comprehensive analysis based on the outcome of this proceeding, the proportional-integral controller coefficients allotted to the current reference design process are enabled to reach their maximum robustness capabilities against any output voltage variation. Moreover, the converter reference current tracking-based assessment leads to several smooth hyperbolic curves with their unique geometric properties. Consequently, the alteration trend of these curves facilitates the Lyapunov coefficients to be adjusted commensurate with the dynamic operation of the converter while converging to zero steady-state errors. Using a TMS320F28335 digital signal processor, disparate experimental results are conducted on the SIDO-TLC to verify the accurate and robust performance of the proposed control strategy.