  Dark energy phenomena has inspired lots of investigations on the cosmological
constant problems. In order to understand its origin and properties as well as
its impacts on universe's evolutions, there are many approaches to modify the
well-known General Relativity, such as the Weyl-Lyra Geometry. In the well
studied cosmology model within Lyra geometry, there is a problem that the first
law of thermodynamics is violated. To unravel this issue, if we use the
effective density and pressure in the Lyra cosmology model to preserve the
first law of thermodynamics in the cosmos, the former 1-form $(\beta,0,0,0)$
cannot give a proper vacuum behavior. In this paper, the auxiliary 1-form is
modified to overcome this difficulty. It can be shown that the complex terms in
the field equation derived from the regime of Lyra Geometric$
\frac{3}{2}{\phi}^{\mu}{\phi}_{\nu}-\frac{3}{4}{\delta}^{\mu}_{\nu}{\phi}^{\alpha}{\phi}_{\alpha}$with
our new 1-form could behave just as the cosmological constant. This work can be
regarded as a new exploration on a possible origin of the cosmological constant
from a Lyra cosmology model.
