  In light of the increasing hints of new physics at the muon $g-2$ and
neutrino oscillation experiments, we consider the recently observed tension in
the long-baseline neutrino oscillation experiments as a potential indication of
Lorentz invariance violation. For this purpose, the latest data from T2K and
NO$\nu$A is analysed in presence of non-minimal Lorentz invariance violation.
Indeed, we find that isotropic violation in dimensions $D =$ 4, 5 and 6 can
alleviate the tension in neutrino oscillation data by 0.4$-$2.4$\sigma$ CL
significance, with the isotropic coefficient $\gamma^{(5)}_{\tau \tau} =$
3.58$\times$10$^{-32}$GeV$^{-1}$ yielding the best fit. At the same time, the
anomalous muon $g-2$ result can be reproduced with an additional non-isotropic
violation of $d^{zt} =$ -1.7$\times$10$^{-25}$. The analysis highlights the
possibility of simultaneous relaxation of experimental tensions with Lorentz
invariance violation of mixed nature.
