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 (ET) 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 pp collision energy of 1.96 TeV, and the CDF II detector. We find 42 lgammaET events versus an expectation of 37.3+/-5.4 events. We observe 31 llgamma+X events versus an expectation of 23.0+/-2.7 events. We find no events similar to the run I eegammagammaET event.