  In this paper we study a homothetic vector field of a Bianchi type-I model
based on Lyra geometry. The cases when a displacement vector is function of $t$
and when it is constant are considered. In both two cases we investigate the
equation of state. A comparison between the obtained results, using Lyra
geometry, and that have obtained previously in the context of General
Relativity, based on Riemannian geometry, will be given.
