I was inspired to write SQLite while working with Informix on DDG-79 and I saw how useful an embedded database would be in some situations, compared to a client/server solution. So I went off and wrote SQLite on my own, while the development contract was on hiatus. There was never a request for SQLite or anything like it coming from the the navy (or more precisely, Bath Iron Works) as they were both very happy with Informix on the ship and Oracle on land and had zero desire for anything new or different. The development team I worked on ended up using SQLite some for prototyping and testing on that project, but it was never deployed to the ship, as far as I know.
So yes, the whole point of SQLite was to build a database that operated as a library linked into the application, rather than as a separate server, as ginko postulates. Design issues on a single system within DDG-79 (Automated Common Diagrams) were the inspiration for that idea, but to say that SQLite was designed for DDG-79 is not true. There was never a request for SQLite coming from the navy or the ship designers. Indeed, there is was a lot of pushback against SQLite. SQLite was just a crazy idea coming from a rogue developer who happened to be working on one of the many on-board systems at that time.