  We present results from a high resolution X-ray imaging study of nearby
LINERs observed by Chandra. This study complements and extends previous X-ray
studies of LINERs, focusing on the under-explored population of nearby
dust-enshrouded infrared-bright LINERs. The sample consists of 15 IR-bright
LINERs (L_FIR/L_B > 3), with distances that range from 11 to 26 Mpc. Combining
our sample with previous Chandra studies we find that ~ 51% (28/55) of the
LINERs display compact hard X-ray cores. The nuclear 2-10 keV luminosities of
the galaxies in this expanded sample range from ~ 2 X 10^38 ergs s^-1 to ~ 2 X
10^44 ergs s^-1. We find an intriguing trend in the Eddington ratio vs. L_FIR
and L_FIR/L_B for the AGN-LINERs in the expanded sample that extends over seven
orders of magnitude in L/L_Edd. This correlation may imply a link between black
hole growth, as measured by the Eddington ratio, and the star formation rate
(SFR), as measured by the far-IR luminosity and IR-brightness ratio. If the
far-IR luminosity is an indicator of the molecular gas content in our sample of
LINERs, our results may further indicate that the mass accretion rate scales
with the host galaxy's fuel supply. We discuss the potential implications of
our results in the framework of black hole growth and AGN fueling in low
luminosity AGN. (Abridged)
