  Yb-based magnets, with a perfect triangular lattice of pseudospin-$1/2$
Yb$^{3+}$ ions, have emerged as candidates for realizing a quantum spin-liquid
state, with NaYbS$_2$ being a prominent example. Here we present the
solid-solution series NaYb$_{1-x}$Lu$_{x}$S$_2$ with well-defined single
crystals over the entire substitution range $0\le x\le 1$. Chemical and
structural analysis indicate a statistically homogeneous replacement of
Yb$^{3+}$ by Lu$^{3+}$ ions. We magnetically characterize the relatively small
single crystals using electron spin resonance (ESR). Below $30$K the ESR
intensity can be well described by a Curie-Weiss function for all \textit{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 $2$K 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 NaYb$_{1-x}$Lu$_{x}$S$_2$ as a family of diluted triangular-lattice
spin liquids.
