Simple examples of equivariant cobordism

Let $Y$ be an oriented 3-manifold with a free action by a finite group $G$. If I understand correctly, there exists a multiple of $NY$ of $Y$ and an oriented manifold $X$ such that $partial X = NY$ and $G$ extends to a free action on $X$. (That is, the equivariant oriented cobordism group is finite. Here, I believe $NY$ should be interpreted as $N$ disjoint copies of $Y$ – note that $N$ is nonzero.) I am trying to understand some very simple examples of this. For instance, if $Y = S^3$ and $G$ is a cyclic group (so that the quotient is a lens space), what is the manifold $X$?

EDIT: For a concrete mention of this claim, see the bottom of the first page of https://www.maths.ed.ac.uk/~v1ranick/papers/aps002.pdf

I realize that the claim is from equivariant bordism theory (as mentioned in one of the comments) but I am not very familiar with this, so I just gave the place where I first saw it.