Combining tight-binding theory, atom manipulation, and scanning tunneling spectroscopy, we demonstrate a quasicontinuous tuning of the flat-band energy in cluster-decorated Lieb lattices. By substituting the edge sites of Lieb lattices with tunable, rhombus-shaped four-site clusters, the emergent flat bands inherit the eigenenergies of the clusters and can be smoothly and predictably adjusted over a wide range, as verified experimentally with Fe atomic lattices on Ag(111). Our approach enables precise alignment of the flat-band energy with the Fermi level while preserving graph connectivity, providing a convenient and reliable platform for exploring emerging phenomena in quantum materials.

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• Flat bands
• Local density of states
• Scanning tunneling spectroscopy
• Tight-binding model