Yb-based magnets, with a perfect triangular lattice of pseudospin-12Yb3+ ions, have emerged as candidates for realizing a quantum spin-liquid state, with NaYbS2 being a prominent example. Here, we present the solid-solution series NaYb1-xLuxS2 with well-defined single crystals over the entire substitution range 0=x=1. Chemical and structural analysis indicate a statistically homogeneous replacement of Yb3+ by Lu3+ ions. We magnetically characterize the relatively small single crystals using electron spin resonance (ESR). Below 30K, the ESR intensity can be well described by a Curie-Weiss function for all x, with a decreasing Weiss temperature with increasing Lu content. This reduction of the average magnetic interaction upon Lu substitution is also supported by magnetization measurements. Importantly, no signs of magnetic or spin-glass order are detected down to 2K for any x. For x>0.5, the ESR linewidth strongly increases, indicating the breakup of the magnetic system into disconnected clusters, as expected from percolation physics. The experimental magnetization data are found to be in good agreement for all x with results of classical Monte Carlo simulations for a triangular-lattice Heisenberg model, amended with a small second-neighbor interaction. Taken together, our results establish NaYb1-xLuxS2 as a family of diluted triangular-lattice spin liquids.