You can export the lottie.json file in two ways:
1- From the [Publish] modal, by clicking any option under "Mobile".
2- You can also use the top menu: Project > Export > Lottie
Tip: You can export your Lottie file through the top menu while you are offline!
Note: Subcomponents not animating in a Lottie export is expected. The only way to get subcomponents to play is to render the component in a browser. The same goes for Video and GIF.