The Lambek-Grishin calculus LG is a categorial grammar obtained by turning the one-sided sequents of the non-associative Lambek calculus NL into two-sided sequents, and adding interaction postulates between the two families of connectives thus obtained. In this paper, we prove a new lower bound on the generative capacity of LG, namely the class of languages that are the intersection of a context-free language and the permutation closure of a context-free language. This implies that LG

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... languages like {a n b n c n d n e n | n ∈ N} and the permutation closure of {a n b n c n | n ∈ N}.