Sounds like you have distributed uses with local desktop applications, and you want to have them enter and save data into a shared database.
The client desktop applications can simply connect to a database server using TCP. You can't use Sqlite for this, as it is a file-based database and not a database server. You could use PostgreSql though.
Other options:
local database server on each client computer that synchronizes with master databases or other client databases using replication. Generally speaking, these should all be the same "brand" of database.
local file database on each client computer (such as sqlite) that synchronizes with master database or other client databases using a tool like SymmetricDS or Daffodil which lets you sync different databases over HTTP.