I have read their limits FAQ, they talk about many limits except limit of the whole database.
Though this is an old question, but let me share my findings for people who reach this question.
Although Sqlite documentation states that maximum size of database file is ~140 terabytes but your OS imposes its own restrictions on maximum file size for any type of file.
For e.g. if you are using FAT32 disk on Windows, maximum file size that I could achieve for sqLite db file was 2GB. (According to Microsoft site, limit on FAT 32 system is 4GB but still my sqlite db size was restricted to 2GB). While on Linux , I was able to reach 3 GB (where I stopped. it could have reached more size)
NOTE: I had written a small java program that will start populating sqlite db from 0 rows and go on populating until stop command is given.