  This paper is devoted to investigate the recently proposed modified
Gauss-Bonnet $f(\mathcal{G},T)$ gravity, with $\mathcal{G}$, the Gauss-Bonnet
term, coupled with ${T}$, the trace of energy-momentum tensor. We have used the
Noether symmetry methodology to discuss some cosmologically important
$f(\mathcal{G},T)$ gravity models with anisotropic background. In particular,
the Noether symmetry equations for modified $f(\mathcal{G},T)$ gravity are
reported for locally rotationally symmetric Bianchi type $I$ universe.
Explicitly, two models have been proposed to explore the exact solutions and
the conserved quantities. It is concluded that the specific models of modified
Gauss-Bonnet gravity may be used to reconstruct $\Lambda$CDM cosmology without
involving any cosmological constant.
