Present paper is the study of the anisotropic spatially Bianchi type-I (B-I) homgeneous cosmological models in the chassis of normal gauge for Lyra's manifold. A deterministic solution has been obtained by taking de- celeration parameter to be dependent on time which results in average scale factor has been obtained. Modified field equations given by Einstein for the homogeneous Binachi Type I metric are solved. Our models are in accelerating phase which is consistent to the recent observations. It has been found that the displacement vector behaves like cosmological term in the normal gauge treatment and the solutions are consistent with recent observations of SNe Ia. It has been found that massive strings dominate in the decelerating universe whereas strings dominate in the accelerating universe. The strings dominate in the early universe and eventually disappear from the universe for sufficiently large times. This is in consistent with the current observations. Some physical and geometric behaviour of these models are also discussed.