Generalization of $\lambda$-directedness

Question

It is well known that objects in $\mathbb{Set}$ whose hom-functors preserve $\lambda$-directed colimits,i.e. colimits whose schemes are $\lambda$-directed posets are those sets whose cardinality is $<\lambda$. My question is how do look sets whose hom-functors preserve colimits whose schemes are linearly ordered posets of length $\lambda$ ? I.e. especially not necessarily well-ordered posets.