Given a category $\mathcal{C}$, it follows from Proposition 4.1 of Day's

Brian Day, Limit spaces and closed span categories, Lecture Notes in Mathematics, 420, 1974 (doi:10.1007/BFb0063100).

That the bicategory $\mathsf{Span}_\mathcal{C}$ of spans in $\mathcal{C}$ has right Kan extensions and right Kan lifts iff $\mathcal{C}$ is locally Cartesian closed.

1. Does $\mathsf{Span}_\mathcal{C}$ also have left Kan extensions and left Kan lifts if (and perhaps only if?) $\mathcal{C}$ is locally Cartesian closed too?
2. What would be explicit descriptions for $\mathsf{Ran}$ and $\mathsf{Rift}$ in $\mathsf{Span}_{\mathcal{C}}$? What about for $\mathsf{Lan}$ and $\mathsf{Lift}$ if these also exist?

Note: One fact I've thought about exploiting is using the isomorphism $$\mathsf{Span}_\mathcal{C}(A,B)\cong\mathcal{C}_{/A}\times_{\mathcal{C}}\mathcal{C}_{/B},$$ where the functors $\mathcal{C}_{/A},\mathcal{C}_{/B}\to\mathcal{C}$ in the pullback are the forgetful ones, together with the fact that $2$-pullbacks are $2$-functorial, and that $2$-functors preserve internal adjunctions as a means of transferring the dependent sum/change of base/dependent product adjunction $$\Sigma_f\dashv f^*\dashv\Pi_f\colon\mathcal{C}_{/A}\underset{\scriptstyle\leftarrow}{\leftrightarrows}\mathcal{C}_{/B}$$ associated to any morphism $f\colon A\to B$ of $\mathcal{C}$ that comes from $\mathcal{C}$ being locally Cartesian closed so as to obtain e.g. a functor $$\mathsf{Ran}_\lambda\colon\underbrace{\mathsf{Span}_{\mathcal{C}}(A,X)}_{=\mathcal{C}_{/A}\,\times_{\mathcal{C}}\,\mathcal{C}_{/X}}\to\underbrace{\mathsf{Span}_{\mathcal{C}}(B,X)}_{=\mathcal{C}_{/B}\,\times_{\mathcal{C}}\,\mathcal{C}_{/X}}$$ right adjoint to precomposition by a span $\lambda$ (corresponding to base change $f^*$), but am a bit confused about how the details would work here.