This work presents the properties of 42 objects in the group of the most luminous, highest star formation rate (SFR) low-ionization nuclear emission-line regions (LINERs) at z=0.04-0.11. We obtained long-slit spectroscopy of the nuclear regions for all sources, and FIR data (Herschel and IRAS) for 13 of them. We measured emission-line intensities, extinction, stellar populations, stellar masses, ages, active galactic nuclei (AGN) luminosities, and SFRs. We find considerable differences from other low-redshift LINERs, in terms of extinction, and general similarity to star-forming galaxies. We confirm the existence of such luminous LINERs in the local universe, after being previously detected at z~0.3 by Tommasin et al. The median stellar mass of these LINERs corresponds to 6-7x10^10^M_{sun}_ which was found in previous work to correspond to the peak of relative growth rate of stellar populations and therefore for the highest SFRs. Other LINERs although showing similar AGN luminosities have lower SFR. We find that most of these sources have LAGN~LSF suggesting co-evolution of black hole and stellar mass. In general, the fraction of local LINERs on the main sequence of star-forming galaxies is related to their AGN luminosity.