We investigate the time-dependent nature of the cosmological constant, Lambda, of the Einstein Field Equation (EFE). Beginning with the Einstein-Hilbert action as our fundamental principle we develop a modified version of the EFE allowing the value of Lambda to vary as a function of time, Lambda (t), indirectly, for an expanding universe. We follow the evolving Lambda presuming four-dimensional space-time and a flat universe geometry and present derivations of Lambda (t) as functions of the Hubble constant, matter density, and volume changes which can be traced back to the radiation epoch. The models are more detailed descriptions of the Lambda dependence on cosmological factors than previous, allowing calculations of the important parameters, Omega(m) and Omega(r), to deep lookback times. Since we derive these without the need for extra dimensions or other special conditions our derivations are useful for model evaluation with astronomical data. This should aid resolution of several difficult problems of astronomy such as the best value for the Hubble constant at present and at recombination.