because of the Gorenstein assumption.

    If $\Lambda$ has a node at $x$ then $x$ is a smooth point of $X$ or $(X, \Lambda)$ is a general hyperplane section of a cyclic quotient singularity. In the minimal log resolution the dual graph of the exceptional curves is $$\bullet   \ {-}\ c_1  \ -\ \cdots  \ - \ c_n  \ {-}
    \ \bullet \qquad (c_i\geq1),$$ where $c_i$ represents a smooth rational curve of self-intersection $-c_i$ and each $\bullet$ represents a (local) component of the strict transform of $\Lambda$. If $c_i=1$ for some $i$ then $n=1$ and $\Lambda$ is a normal crossing divisor in a smooth surface.

non-normal Gorenstein slc singularities, $\Lambda=0$

:   We describe the dual graph of the $f$-exceptional divisors over $x$: analytically locally $X$ consists of $k$ irreducible components, on each component we have a resolution graph as in the previous item, and these are glued together where the components intersect. In total we have a cycle of smooth rational curve.

non-normal Gorenstein slc singularities, $\Lambda\neq 0$

:   The difference to the previous case is that the local components are now glued in a chain and the ends of the chain intersect the strict transform of the boundary. In this 