The standard ΛCDM model is reasonably successful in describing the universe, and is the most widely acceptable model in cosmology. However, there are several theoretical issues, such as the initial singularity, the cosmological constant problem, the particle nature of dark matter, the existence of anomalies in the cosmic microwave background radiation and on small scales, the predictions and tests of the inflationary scenario, and whether general relativity is valid on the largest possible scales. Hence there is growing interest in looking at modified theories. In this presentation, a reconstruction is made of the Friedmann-Lemaitre-Robertson-Walker models with a dynamic cosmological parameter in f(R,T) modified gravity. This theory has a number of pleasing features, such as the avoidance of the initial big-bang singularity and a variable cosmological parameter. A dynamic cosmological parameter, which arises naturally in this theory, can solve the cosmological constant problem, and is also a candidate for dark energy. In addition, a variable cosmological parameter fits observations better than the standard ΛCDM model. The model exhibits a transition from deceleration to acceleration. The time evolution of the physical parameters such as energy density, pressure and equation of state are analyzed. Also the energy conditions and an Om(z) diagnostic analysis are discussed.