  In this paper we study the gauge mediation signal with the ATLAS detector at
the CERN LHC. We focus on the case where the NLSP is the long-lived lightest
neutralino ($\tilde{\chi}^0_1$) which decays dominantly into a photon
($\gamma$) and a gravitino ($\tilde{G}$). A non-pointing photon from the
neutralino decay can be detected with good position and time resolutions by the
electormagnetic calorimeter (ECAL), while the photon momentum would be
precisely measured if the photon is converted inside the inner tracking
detector before reaching the ECAL. A new technique is developed to determine
the masses of the slepton ($\tilde{\ell}$) and the neutralino from events with
a lepton and a converted non-pointing photon arising from the cascade decay
$\tilde{\ell}\to \ell\tilde{\chi}^0_1\to \ell\gamma \tilde{G}$. A Monte Carlo
simulation at a sample point shows that the masses would be measured with an
error of 3% for $\cal{O}$(100) selected $\ell\gamma$ pairs. Once the sparticle
masses are determined by this method, the decay time and momentum of the
neutralino are solved using the ECAL data and the lepton momentum only, for all
$\ell\gamma$ pairs without the photon conversion. We estimate the sensitivity
to the neutralino lifetime for $c\tau=10$ cm to $\cal{O}$(10) m.
