Ribbon cobordisms between lens spaces

We determine when there exists a ribbon rational homology cobordism between two connected sums of lens spaces, i.e. one without $3$-handles. In particular, we show that if space $L$ admits to different space, then must be homeomorphic $L(n,1)$, up orientation-reversal. As an application, classify $\chi$-concordances $2$-bridge links. Our work builds on Lisca's embeddings linear lattices.