Speech synthesis (text to speech, TTS) and recognition (automatic speech recognition, ASR) are important speech tasks, and require a large amount of text and speech pairs for model training. However, there are more than 6,000 languages in the world and most languages are lack of speech training data, which poses significant challenges when building TTS and ASR systems for extremely low-resource languages. In this paper, we develop LRSpeech, a TTS and ASR system under the extremely low-resource setting, which can support rare languages with low data cost. LRSpeech consists of three key techniques: 1) pre-training on rich-resource languages and fine-tuning on low-resource languages; 2) dual transformation between TTS and ASR to iteratively boost the accuracy of each other; 3) knowledge distillation to customize the TTS model on a high-quality target-speaker voice and improve the ASR model on multiple voices. We conduct experiments on an experimental language (English) and a truly low-resource language (Lithuanian) to verify the effectiveness of LRSpeech. Experimental results show that LRSpeech 1) achieves high quality for TTS in terms of both intelligibility (more than $98%$ intelligibility rate) and naturalness (above 3.5 mean opinion score (MOS)) of the synthesized speech, which satisfy the requirements for industrial deployment, 2) achieves promising recognition accuracy for ASR, and 3) last but not least, uses extremely low-resource training data. We also conduct comprehensive analyses on LRSpeech with different amounts of data resources, and provide valuable insights and guidances for industrial deployment. We are currently deploying LRSpeech into a commercialized cloud speech service to support TTS on more rare languages.