We present results of a search for anomalous production of events containing a charged lepton (l, either e or mu) and a photon (gamma), both with high transverse momentum, accompanied by additional signatures X, including missing transverse energy (is not an element of(T)) and additional leptons and photons. We use the same selection criteria as in a previous CDF search but with a substantially larger data set, 305 pb(-1), a p (p) over bar collision energy of 1.96 TeV, and the CDF II detector. We find 42 l gamma E(T) events versus an expectation of 37.3 +/- 5.4 events. We observe 31 ll is not an element of gamma+X events versus an expectation of 23.0 +/- 2.7 events. We find no events similar to the run I ll gamma gamma is not an element of(T) event.