  The discrete-time rational Calogero's goldfish system is obtained from the
Ansatz Lax pair. The discrete-time Lagrangians of the system possess the
discrete-time 1-form structure as those in the discrete-time Calogero-Moser
system and discrete-time Ruijsenaars-Schneider system. Performing two steps of
continuum limits, we obtain Lagrangian hierarchy for the system. Expectingly,
the continuous-time Lagrange 1-form structure of the system holds. Furthermore,
the connection to the lattice KP systems is also established.
