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There are programs like sqlitebrowser that let you view databases as tables and edit them in a convenient way. But I can't encounter a similar program for linux console. I have a server that I can access via SSH, and having a convenient database browser for Linux console would be beneficial to me.
Is there such a program offering terminal-compatible "graphical" UI? It could be based on e.g. curses/ncurses/unicurses.
Example for another database engine/OS: 
My choice for browsing tabular data in the console or terminal is [Visidata] (https://www.visidata.org). It works well with SQLite and a variety of other data sources. It does allow editing data in the cells of a table, but is not great for tasks like altering table structures. It does not allow running SQL queries, but is very efficient in browsing data and manipulating it in a variety of ways.
The SQLite package includes the sqlite3 command-line client, which appears to offer equivalent functionality to mysql (MySQL), psql (PostgreSQL) or sqlplus (Oracle). I don't see that it supports network connection, but that is really outside the intended use-case for SQLite and is unnecessary if you have SSH access to the server.
sqlite3executable – or, put into other words, what features do you need it doesn't offer? I could think of e.g. ncurses support or the like (to provide a kind of GUI – see e.g. SQLite Commander), but I cannot tell what you've got in mind :)