The osseointegration in/around additively manufactured (AM) lattice structures of a new titanium alloy, Ti–19Nb–14Zr, was evaluated. Different lattices with increasingly high sidewalls gradually closing them were manufactured and implanted in sheep. After removal, the bone–interface implant (BII) and bone–implant contact (BIC) were studied from 3D X-ray computed tomography images. Measured BII of less than 10 µm and BIC of 95% are evidence of excellent osseointegration. Since AM naturally leads to a high-roughness surface finish, the wettability of the implant is increased. The new alloy possesses an increased affinity to the bone. The lattice provides crevices in which the biological tissue can jump in and cling. The combination of these factors is pushing ossification beyond its natural limits. Therefore, the quality and speed of the ossification and osseointegration in/around these Ti–19Nb–14Zr laterally closed lattice implants open the possibility of bone spline key of prostheses. This enables the stabilization of the implant into the bone while keeping the possibility of punctual hooks allowing the implant to be removed more easily if required. Thus, this new titanium alloy and such laterally closed lattice structures are appropriate candidates to be implemented in a new generation of implants.