We study quintessence cosmology with an effective Λ-term in Lyra manifold.We consider three different models by choosing variable Λ depending on time,the Hubble parameter and the energy density of dark matter and dark energy.Dark energy is assumed as quintessence which interacts with the dark matter.Using numerical analysis we investigate the behavior of cosmological parameters in three different models and compare our results with observational data.State-finder diagnostic is also performed for all models.