  We describe a presentation for the augmented fundamental rack of a link in
the lens space $L(p,1)$. Using this presentation, the (enhanced) counting rack
invariants that have been defined for the classical links are applied to the
links in $L(p,1)$. In this case, the counting rack invariants also include the
information about the action of $\pi_{1}(L(p,1))$ on the augmented fundamental
rack of a link.
