I have read their limits faq, they talk about many limits except limit of the whole database.
This is fairly easy to deduce from the implementation limits page:
An SQLite database file is organized as pages. The size of each page is a power of 2 between 512 and SQLITE_MAX_PAGE_SIZE. The default value for SQLITE_MAX_PAGE_SIZE is 32768.
...
The SQLITE_MAX_PAGE_COUNT parameter, which is normally set to 1073741823, is the maximum number of pages allowed in a single database file. An attempt to insert new data that would cause the database file to grow larger than this will return SQLITE_FULL.
So we have 32768 * 1073741823, which is 35,184,372,056,064 (35 trillion bytes)!
You can modify SQLITE_MAX_PAGE_COUNT
or SQLITE_MAX_PAGE_SIZE
in the source, but this of course will require a custom build of SQLite for your application. As far as I'm aware, there's no way to set a limit programmatically other than at compile time (but I'd be happy to be proven wrong).