  We present Herschel/PACS observations of extended [CII]157.7{\mu}m line
emission detected on ~ 1 - 10 kpc scales in 60 local luminous infrared galaxies
(LIRGs) from the Great Observatories All-sky LIRG Survey (GOALS). We find that
most of the extra-nuclear emission show [CII]/FIR ratios >~ 4 x 10^-3, larger
than the mean ratio seen in the nuclei, and similar to those found in the
extended disks of normal star-forming galaxies and the diffuse inter-stellar
medium (ISM) of our Galaxy. The [CII] "deficits" found in the most luminous
local LIRGs are therefore restricted to their nuclei. There is a trend for
LIRGs with warmer nuclei to show larger differences between their nuclear and
extra-nuclear [CII]/FIR ratios. We find an anti-correlation between [CII]/FIR
and the luminosity surface density, {\Sigma}_IR, for the extended emission in
the spatially-resolved galaxies. However, there is an offset between this trend
and that found for the LIRG nuclei. We use this offset to derive a beam
filling-factor for the star-forming regions within the LIRG disks of ~ 6 %
relative to their nuclei. We confront the observed trend to photo-dissociation
region (PDR) models and find that the slope of the correlation is much
shallower than the model predictions. Finally, we compare the correlation found
between [CII]/FIR and {\Sigma}_IR with measurements of high-redshift
starbursting IR-luminous galaxies.
