Lithium oxide is a possible candidate for a breeder blanket material in fusion reactors. Tritium is generated in the material, which can be extracted and fed into the fusion reactor to help sustain the fusion reaction. Experimental studies have shown the extraction rate is controlled by diffusion of tritium in the bulk, but the exact mechanism is not clear. Here we present ab initio density functional calculations of the various diffusion pathways which have been suggested, including the diffusion of tritium as an interstitial and various vacancy assisted mechanisms. The activation energy has been calculated for each pathway, and by comparison with experimental results we have deduced which mechanism is most likely. This is shown to be a simple two-stage swapping of a lithium and tritium ion.