Let $I, J$ be categories and $\varphi : I \to J$ a functor, then we have a pullback functor $\varphi^* : \mathcal{C}^J \to \mathcal{C}^I$. The left and right Kan extensions along $\varphi$, denoted by $\operatorname{Lan}$ and $\operatorname{Ran}$, give the left and right adjoints of $\varphi^*$ respectively.
When studying the Simplicial Homotopy Theory, I found that there are some functors whose left Kan extensions are exactly $\operatorname{id}$'s. For example, consider the Yoneda embedding of simplex category $\Delta$: \begin{align*} h_{\Delta} : \Delta & \longrightarrow \mathsf{Set}_{\Delta} := \operatorname{Fct} (\Delta^{\mathrm{op}}, \mathsf{Set} ) \\ [n] & \longmapsto \Delta^n := \operatorname{Hom}_{\Delta} (\cdot, [n]). \end{align*} Its left Kan extension along $h_{\Delta} : \Delta \to \mathsf{Set}_{\Delta}$ satisfies that for all $K \in \mathsf{Set}_\Delta$, $$ \operatorname{Lan} (h_{\Delta}) (K) = \varinjlim h_{\Delta} \big|_{(h_{\Delta} / K) } \simeq K. $$ Hence $\operatorname{Lan} (h_{\Delta}) \simeq \operatorname{id}$.
However, I think that in general this is not true. Because ( let $\mathcal{C} = J$ ) \begin{align*} \operatorname{Hom}_{J^J} (\cdot, \operatorname{Ran} (\varphi)) & \simeq \operatorname{Hom}_{J^I} ( \varphi^*(\cdot), \varphi ) \\ & \simeq \operatorname{Hom}_{J^I} ( (\cdot) \circ \varphi, \varphi ), \end{align*} which in general $\not \simeq \operatorname{Hom}_{J^J} ( \cdot, \operatorname{id}_J )$, I think.
So my question is (I browsed through several books on category theory, MSE and MO, but found no answers):
When does $\operatorname{Lan} (\varphi) = \operatorname{id}_J$, and when does $\operatorname{Ran}(\varphi)$?
In general, what does $\operatorname{Ran}(\varphi)$ and $\operatorname{Lan}(\varphi)$ look like?