We present a new positive kinetic scheme built on the efficient collide-and-stream algorithm of the lattice Boltzmann method (LBM) to address the compressible Euler equations with strong discontinuities. Starting from previous work on relaxation methods, we show how the LBM discretization can yield a second-order scheme, referred to as vectorial LBM. In order to keep the solution in a convex domain, we develop a monolithic blending strategy that preserves the simplicity of the algorithm. This approach employs convex limiters, carefully designed to ensure either positivity of the density and the internal energy or well-defined maximum principles, while minimizing numerical dissipation. On challenging test cases involving near-vacuum regions, we demonstrate the scheme accuracy, robustness, and ability to capture sharp discontinuities with minimal numerical oscillations.