I have 3 SQLite DBs, each having exactly the same set of 7 tables with respect to table structure. [They are Log Dumps from 3 different Machines].
I want to combine them
Export each database to an SQL dump and then import the dumps into your new combined database.
For GUIs have a look at http://www.sqlite.org/cvstrac/wiki?p=ManagementTools
For example, with SQLiteStudio that will be Database > Export the database: Export format: SQL > Done.