Colimits of a diagram over an ordinal number

Question

The context for my question is the following:

The class $l(F)$ of morphisms which have the left lifting property with respect to $F$ is stable under transfinite compositions.

I was able to prove that $\varinjlim_{i < \mu} X(i) = X(\lambda)$ whenever $\mu = \lambda + 1$. I suspect that $\varinjlim_{i < \mu} X(i) = X(\mu)$ when $\mu$ is a limit ordinal, but I don't know how to prove it. Any help is welcome.