In recent years, the R-Process Alliance (RPA) has conducted a successful search for stars that are enhanced in elements produced by the rapid neutron-capture (r-)process. In particular, the RPA has uncovered a number of stars that are strongly enriched in light r-process elements, such as Sr, Y, and Zr. These so-called limited-r stars were investigated to explore the astrophysical production site(s) of these elements. We investigate the possible formation sites for light neutron-capture elements by deriving detailed abundances for neutron-capture elements from high-resolution spectra with a high signal-to-noise ratio of three limited-r stars. We conducted a kinematic analysis and a 1D local thermodynamic equilibrium spectroscopic abundance analysis of three stars. Furthermore, we calculated the lanthanide mass fraction (XLa) of our stars and of limited-r stars from the literature. We found that the abundance pattern of neutron-capture elements of limited-r stars behaves differently depending on their [Ba/Eu] ratios, and we suggest that this should be taken into account in future investigations of their abundances. Furthermore, we found that the XLa of limited-r stars is lower than that of the kilonova AT2017gfo. The latter seems to be in the transition zone between limited-r XLa and that of r-I and r-II stars. Finally, we found that unlike r-I and r-II stars, the current sample of limited-r stars is largely born in the Galaxy and is not accreted.