Result of LexBFS on an outer-planar graph

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Suppose we have an outer-planar graph $G$. Is the following expression true? If yes, please prove it. If no, please give a counterexample.

After running LexBFS on $G$, we will have a vertex order $v_1,...,v_n$ so that $\forall i: indeg(v_i)\leq2$.