The availability of parallel texts is crucial to the performance of machine translation models. However, most of the world's languages face the predominant challenge of data scarcity. In this paper, we propose strategies to synthesize parallel data relying on morpho-syntactic information and using bilingual lexicons along with a small amount of seed parallel data. Our methodology adheres to a realistic scenario backed by the small parallel seed data. It is linguistically informed, as it aims to create augmented data that is more likely to be grammatically correct. We analyze how our synthetic data can be combined with raw parallel data and demonstrate a consistent improvement in performance in our experiments on 14 languages (28 English <-> X pairs) ranging from well- to very low-resource ones. Our method leads to improvements even when using only five seed sentences and a bilingual lexicon.