Lax comma categories of ordered sets

Let $\mathsf{O}\mathsf{r}\mathsf{d}$ be the category of (pre)ordered sets. Unlike $\mathsf{O}\mathsf{r}\mathsf{d}\mathrm{/}X$, whose behaviour is well-known, not much can be found in the literature about the lax comma 2-category $\mathsf{O}\mathsf{r}\mathsf{d}\mathrm{/}\mathrm{/}X$. In this paper we show that the forgetful functor $\mathsf{O}\mathsf{r}\mathsf{d}\mathrm{/}\mathrm{/}X\to \mathsf{O}\mathsf{r}\mathsf{d}$ is topological if and only if $X$ is complete. Moreover, under suitable hypothesis, $\mathsf{O}\mathsf{r}\mathsf{d}\mathrm{/}\mathrm{/}X$ is complete and cartesian closed if and only if $X$ is. We end by analysing descent in this category. Namely, when $X$ is complete and cartesian closed, we show that, for a morphism in $\mathsf{O}\mathsf{r}\mathsf{d}\mathrm{/}\mathrm{/}X$, being pointwise effective for descent in $\mathsf{O}\mathsf{r}\mathsf{d}$ is sufficient, while being effective for descent in $\mathsf{O}\mathsf{r}\mathsf{d}$ is necessary, to be effective for descent in $\mathsf{O}\mathsf{r}\mathsf{d}\mathrm{/}\mathrm{/}X$.