  The present work deals with scalar field cosmology in the framework of a
quantum gravity modified Einstein-Hilbert Lagrangian with variable $G$ and
$\Lambda$. Using Renormalization group, variable $G$ behaves as a minimally
coupled filed (not the scalar-tensor theory) and variable $\Lambda$ can be
interpreted as a potential function. The point Lagrangian for this model in the
background of homogeneous and isotropic flat FLRW space-time model experiences
point-like Noether symmetry and equivalent potential function $\Lambda(G)$ is
determined. Using a point transformation in the $3D$ augmented space is found
that one of the variable become cyclic and as a consequence there is
considerable simplification to the physical system. Lastly, the constants of
motion can be written in compact form and it is possible to have analytic
cosmological solutions in the present context.
