  The Large Area Telescope (LAT) on board the \Fermi Gamma-ray Space Telescope
(\Fermi) shows long-lasting high-energy emission in many gamma-ray bursts
(GRBs), similar to X-ray afterglows observed by the Neil Gehrels Swift
Observatory \citep[\textit{Swift};][]{gehrels2004}. Some LAT light curves (LCs)
show a late-time flattening reminiscent of X-ray plateaus. We explore the
presence of plateaus in LAT temporally extended emission analyzing GRBs from
the second \lat GRB Catalog \citep[2FLGC;][]{Ajello2019apj} from 2008 to May
2016 with known redshifts, and check whether they follow closure relations
corresponding to 4 distinct astrophysical environments predicted by the
external forward shock (ES) model. We find that three LCs can be fit by the
same phenomenological model used to fit X-ray plateaus \citep{Willingale2007}
and show tentative evidence for the existence of plateaus in their high-energy
extended emission. The most favorable scenario is a slow cooling regime,
whereas the preferred density profile for each GRBs varies from a constant
density ISM to a $r^{-2}$ wind environment. We also compare the end time of the
plateaus in $\gamma$-rays and X-rays using a statistical comparison with 222
\textit{Swift} GRBs with plateaus and known redshifts from January 2005 to
August 2019. Within this comparison, the case of GRB 090510 shows an indication
of chromaticity at the end time of the plateau. Finally, we update the 3-D
fundamental plane relation among the rest frame end time of the plateau, its
correspondent luminosity, and the peak prompt luminosity for 222 GRBs observed
by \textit{Swift}. We find that these three LAT GRBs follow this relation.
