  Context: Stars with about 1$-$2 solar masses at the red giant branch (RGB)
represent an intriguing period of stellar evolution, i.e. when the convective
envelope interacts with the fast-rotating core. During these mixing episodes
freshly synthesized lithium can come up to the stellar surface along with high
angular momentum material. This high angular momentum may alter the surface
rotation pattern.
  Aims: The single rapidly rotating K-giant V1192 Ori is revisited to determine
its surface differential rotation, lithium abundance, and basic stellar
properties such as a precise rotation period. The aim is to independently
verify the antisolar differential rotation of the star and possibly find a
connection to the surface lithium abundance.
  Methods: We applied time-series Doppler imaging to a new multi-epoch data
set. Altogether we reconstructed 11 Doppler images from spectroscopic data
collected with the STELLA robotic telescope between 2007--2016. We used our
inversion code iMap to reconstruct all stellar surface maps. We extracted the
differential rotation from these images by tracing systematic spot migration as
a function of stellar latitude from consecutive image cross-correlations.
  Results: The position of V1192 Ori in the Hertzsprung-Russell diagram
suggests that the star is in the helium core-burning phase just leaving the RGB
bump. We measure $A({\rm Li})_{\rm NLTE}=1.27$, i.e. a value close to the
anticipated transition value of 1.5 from Li-normal to Li-rich giants. Doppler
images reveal extended dark areas arranged quasi-evenly along an equatorial
belt. No cool polar spot is found during the investigated epoch. Spot
displacements clearly suggest antisolar surface differential rotation with
$\alpha=-0.11\pm0.02$ shear coefficient.
  Conclusions: The surface Li enrichment and the peculiar surface rotation
pattern may indicate a common origin.
