  We are interested by the study of several toy models of the Universe in
presence of interacting quintessence DE models. Models are considered in the
cosmology with an Effective varying $\Lambda$-Term in Lyra Manifold. The
motivation of the phenomenological models discussed in this paper is to obtain
corresponding models to describe and understand an accelerated expansion of the
Universe for the later stage of evolution. Phenomenology of the models
describes by the phenomenological forms of $\Lambda(t)$ ($8 \pi G =c =1$).
Concerning to the mathematical hardness we discuss results numerically and
graphically. Obtained results give us hope that proposed models can work as
good models for old Universe and in good agreement with observational data.
