A rigorous first principles Boltzmann-Peierls equation (BPE) for phonon transport approach is employed to examine the lattice thermal conductivity, κL, of strained and unstrained graphene. First principles calculations show that the out-of-plane, flexural acoustic phonons provide the dominant contribution to κL of graphene for all strains, temperatures, and system sizes considered, supporting a previous prediction that used an optimized Tersoff empirical interatomic potential. For the range of finite system sizes considered, we show that the κL of graphene is relatively insensitive to strain. This provides validation for use of the BPE approach to calculate κL for unstrained graphene, which has recently been called into question. The temperature and system size dependence of the calculated κL of graphene is in good agreement with experimental data. The enhancement of κL with isotopic purification is found to be relatively small due to strong anharmonic phonon-phonon scattering. This work provides insight into the nature of phonon thermal transport in graphene, and it demonstrates the power of first principles thermal transport techniques.