In this paper we present a new 3D line alignment technique that can be used in limited resourced MAVs for performing loop closures as well as mutual localisation between MAVs. We identify pairs of 3D line matches from RGB-D frames and find the optimal transformation which aligns these two line sets onto each other in order to find the corresponding relative pose. The alignment of the two 3D line sets are achieved by converting each line match into two matching point pairs and then subjecting them to a least squares minimization process. As we only maintain line features extracted from key frames, our method does not require large memory, high processing power nor a high communication bandwidth between robots. We validate our 3D line alignment technique by performing loop closures and mutual localisation on real-world datasets.