LaTex, 14 pages.The effects of a non-vanishing value for the cosmological constant in the scenario of Lorentz symmetry breaking recently proposed by Cohen and Glashow (which they denote as Very Special Relativity) are explored and observable consequences are pointed out.This work has been partially supported by the European Commission (HPRN-CT-200-00148) and by FPA2003-04597 (DGI del MCyT, Spain), Proyecto HEPHACOS ; P-ESP-00346 (CAM) and Consolider project CSD 2007-00060 (MEC) (Physics of the Accelerated Universe). R.V. is supported by a MEC grant, AP2006-01876.