  We use the distribution formalism to derive the complete set of junction
conditions for general Local Rotationally Symmetric (LRS) spacetimes in the
$1+1+2$ covariant formalism. We start by developing a parametric framework
encompassing timelike, spacelike, or null hypersurfaces. We then introduce the
distribution formalism in the $1+1+2$ framework and obtain the necessary
conditions to preserve the regularity of the $1+1+2$ equations at the
separation hypersurface. Using these results, we can deduce some general
prescriptions on the junction of LRS spacetimes and the properties of the shell
in the non-smooth cases. As examples of the application of the junction
conditions, we use this formalism to perform the matching necessary to obtain
well-known solutions, e.g., the Martinez thin-shell, the Schwarzschild
constant-density fluid star, and the Oppenheimer-Snyder collapse.
