The indication from Dropbox is that this decodes very quickly (faster than bandwidth on the wire to the client). In other words - the storage medium is Lepton, the images are decoded as they are sent to the client from the server. FTA:
Lepton can decompress significantly faster than line-speed for typical consumer and business connections. Lepton is a fully streamable format, meaning the decompression can be applied to any file as that file is being transferred over the network. Hence, streaming overlaps the computational work of the decompression with the file transfer itself, hiding latency from the user.
The compression for storage is transparent to the user - they only see a JPG as requested. On the server side the storage is Lepton. My thought was a possible task to compress images as uploaded and store them as Lepton, then logic to decompress as requested by clients.
In fact, this appears to be the use-case for Dropbox themselves. They are storing the files on-disk in Lepton, and streaming the decompressed JPG as they are requested.