The {\it{Cosmological Boundary Flux Parameter}} is a novel proposal that attempts to explain the origin of the cosmological parameter $\Lambda$ purely by geometric nature. Then we implement this new approach to a flat FLRW universe, along with a barotropic fluid. We present an ansatz in which $\Lambda$ couples straightforwardly to the matter sector; therefore only one extra parameter was introduced: $\lambda$. Also, through a statistical analysis, using late time data of Observational Hubble and type Ia Supernovae, we computed the best-fit value of the free parameters by means of the affine-invariant MCMC. We want to emphasize that the Joint analysis produces a smaller $H_{0}=71.51\rm\,\, Km \,s^{-1}\,Mpc^{-1}$ in contrast to the $\Lambda$CDM result $H_{0}=72.15\rm\,\, Km \,s^{-1}\,Mpc^{-1}$. Indeed, this outcome approaches more to the CMB value $H_{0}^{\rm CMB}=67.70\rm\,\, Km \,s^{-1}\,Mpc^{-1}$ (Planck + BAO). Thus, this might suggest that our propoal might be a good candidate to amend the $H_{0}$ tension. In spite of that, more statistical analysis needs to be done to be certain about this. The work here presented seeks to contribute to the discussion of the possible explanation for the cosmos' acceleration, together with tackling other important questions in modern cosmology.