Living organism are not in equilibrium because work cannot be performed by a system at equilibrium. The living organisms exist in a steady state characterised by concentration of each of the biomolecules.
These biomolecules are in a metabolic flux. Any chemical or physical process moves simultaneously to equilibrium. Living organisms work continuously and they cannot afford to reach equilibrium. The living state thus is an a non-equilibrium steady-state to be able to perform work. This achieved by energy input provided by metabolism.