  In this paper, we study quintessence cosmology with an effective
$\Lambda$-term in Lyra manifold. We consider three different models by choosing
variable $\Lambda$ depend on time, the Hubble parameter and the energy density
of dark matter and dark energy. Dark energy assumed as quintessence which
interacts with the dark matter. By using numerical analysis we investigate
behavior of cosmological parameters in three different models and compare our
results with observational data. Statefinder diagnostic is also performed for
all models.
