  We investigate Scattering amplitudes of the reversible $\theta$-exact
Seiberg-Witten (SW) map based noncommutative (NC) quantum electrodynamics, and
show explicitly the SW map invariance for all tree-level NCQED $2\to2$
proceses, including M\"oller, Bhabha, Compton, pair annihilation, pair
production and light-by-light $(\gamma\gamma\to\gamma\gamma)$ scatterings. We
apply our NCQED results to the $\gamma\gamma\to\gamma\gamma$ and
$\gamma\gamma\to\ell^+\ell^-$ exclusive processes, convoluted to the
ultraperipheral lead $^{208}$Pb ion-ion collisions, recently measured by the
ATLAS collaboration at LHC. We demonstrate that $\gamma\gamma\to\gamma\gamma$
is the more appropriate channel to probe NC scale $\Lambda_{\rm NC}$ while both
are less efficient than some other probes.
