is this an example of nominal unification?
Sure, these unify under nominal unification.  You get a unifier like $X = (b\ a)\bullet\lambda c.c$ which simplifies to $X = \lambda c.c$.  Figures 1 and 3 of Nominal Unification describe the relevant details of the algorithm.  In particular the transitions will be $\approx?$-abstraction-2 and $\approx?$-variable followed by $\#?$-abstraction-2 and $\#?$-atom.