I'm wondering that is there any equivocal commitment scheme (i.e., trapdoor commitment) can be constructed from lattice-based assumptions? I know there are a lot of commitment schemes from lattices as described in More Efficient Commitments from Structured Lattice Assumptions (described in the introduction) but I do not identify any trapdoor commitment scheme from lattice-based assumptions. Thus I'm wondering is there any equivocal commitment scheme? Recall that Pedersen commitment is an equivocal commitment but is constructed from Discrete Log assumption.
If you have a (standard) commitment scheme $C$ and zero-knowledge proofs of knowledge (both exist from LWE -- in fact, both exist from one-way functions), then you necessarily have equivocal commitments. Here is a straightforward equivocal commitment $C_e$: committing with $C_e$ is just committing with $C$, and opening a commitment is done by revealing the committed value $m$, together with a proof of knowledge of an opening to $C$ such that the commitment opens to $m$. It is easy to see that the proof of knowledge property implies that $C_e$ is binding, and the zero-knowledge property implies the existence of a simulator which can fake proofs of opening to any $m$, hence the commitment is equivocal.
That being said, I'm pretty sure there are many direct and relatively efficient constructions of equivocal commitments. For example, the LWE-based fully homomorphic trapdoor functions from this paper are in particular equivocal commitments (see page 5 of the paper).