  The aim of this article is to explore a potential usability of a
photon-photon self-interaction from the noncommutative quantum electrodynamics
(NCQED) in the case of light-by-light scattering
($\gamma\gamma\to\gamma\gamma$) in ultraperipheral Pb+Pb collisions, a reaction
measured recently by ATLAS and planned for future experiments in hadron-hadron
colliders. We compute the total cross section from both, the full one-loop
standard model (SM) and the tree-level NCQED amplitudes, in the equivalent
photon approximation with impact parameters, for various noncommutative scales,
$\rm\Lambda_{NC}$, and incoming nuclear spin-energy combinations. We find that
NCQED contribution to the cross section has considerable increase at diphoton
invariant mass range higher than $\rm\Lambda_{NC}$, while the SM contribution
is strongly suppressed in such region. Our results show that the current ATLAS
$\rm\sqrt{s_{NN}} = 5.02$ TeV experiment can only probe $\rm\Lambda_{NC}<100$
GeV region. On the other hand, future hadron-hadron collider proposals could
have the potential to extend to $\rm\Lambda_{NC}\lesssim 300$ GeV region,
making the performance of $\rm Pb+Pb(\gamma\gamma)\to Pb+Pb\gamma\gamma$
scattering on testing space-time noncommutativity close to that of the
previously proposed photon-photon mode of linear electron-positron collider.
