Amongst different existing numerical methods, the lattice Boltzmann method (LBM) has recently acquired a growing interest due to its low computational cost, relatively simple parallelisation and an ability to handle complex geometries. Particularly, these advantages arise thanks to a low-order spatial stencil which is used in lattices with few velocities. However, this leads to an inability of classical LBM to deal with thermal and compressible flows. The appropriate coupling between LBM and a finite difference discretisation of energy equation resulting in fully conservative scheme has been a successful attempt to tackle this limitation. While this development furthermore led to the improvement of the solution in terms of the correct jumps relations recovery across the shock waves, the stabilisation of the method for the applications where flow discontinuities are observed remains a challenge. This work aims to set an appropriate framework to apply LBM to fully compressible flows with discontinuities due to the strong shock waves. This is done by means of blending the LBM numerical schemes with an a posteriori Multi-dimensional Optimal Order Detection (MOOD) paradigm to solve hyperbolic systems of conservation laws in 1D and 2D. The resulting scheme presents second order of accuracy for smooth solutions, essentially non-oscillatory behaviour for irregular ones, and, almost fail-safe property concerning positivity issues. The numerical results on a set of sanity test cases and demanding ones will be presented assessing the appropriate behaviour of the blended scheme.