Understanding the physical properties of Ca-carbonate at high pressure is crucial for comprehending the carbon cycle in the Earth's interior. Recently, a new pyrocarbonate, CaC2O5, has been discovered. In this work, we update the phase diagram of CaC2O5. The structure, elastic, and seismic properties of CaC2O5 polymorphs under lower mantle pressure are studied using first-principles calculations, and compared with those of orthocarbonate Ca2CO4. Our findings reveal that CaC2O5 may have four stable phases under lower mantle temperature and pressure conditions, namely the I42d, Fdd2, Pc, and C2 phases. The carbon may be stored in the new pyrocarbonate CaC2O5 polymorphs. The thermodynamic properties of CaC2O5-I42d are obtained by quasi-harmonic approximation. This work contributes to our understanding of the behavior of Ca-carbonate in the Earth's lower mantle conditions.