Assuming three columns in the table: ID, NAME, ROLE
BAD: This will insert or replace all columns with new values for ID=1:
INSERT OR REPLACE INTO Employee (id, name, role)
VALUES (1, 'John Foo', 'CEO');
BAD: This will insert or replace 2 of the columns... the NAME column will be set to NULL or the default value:
INSERT OR REPLACE INTO Employee (id, role)
VALUES (1, 'code monkey');
GOOD: Use SQLite On conflict clause
UPSERT support in SQLite! UPSERT syntax was added to SQLite with version 3.24.0!
UPSERT is a special syntax addition to INSERT that causes the INSERT to behave as an UPDATE or a no-op if the INSERT would violate a uniqueness constraint. UPSERT is not standard SQL. UPSERT in SQLite follows the syntax established by PostgreSQL.

GOOD but tedious: This will update 2 of the columns.
When ID=1 exists, the NAME will be unaffected.
When ID=1 does not exist, the name will be the default (NULL).
INSERT OR REPLACE INTO Employee (id, role, name)
VALUES ( 1,
'code monkey',
(SELECT name FROM Employee WHERE id = 1)
);
This will update 2 of the columns.
When ID=1 exists, the ROLE will be unaffected.
When ID=1 does not exist, the role will be set to 'Benchwarmer' instead of the default value.
INSERT OR REPLACE INTO Employee (id, name, role)
VALUES ( 1,
'Susan Bar',
COALESCE((SELECT role FROM Employee WHERE id = 1), 'Benchwarmer')
);
Best Solution
Yesterday I released a small site* to track your rep that used a shared SQLite database for all visitors. Unfortunately, even with the modest load that it put on my host it ran quite slowly. This is because the entire database was locked every time someone viewed the page because it contained updates/inserts. I soon switched to MySQL and while I haven't had much time to test it out, it seems much more scaleable than SQLite. I just remember slow page loads and occasionally getting a database locked error when trying to execute queries from the shell in sqlite. That said, I am running another site from SQLite just fine. The difference is that the site is static (i.e. I'm the only one that can change the database) and so it works just fine for concurrent reads. Moral of the story: only use SQLite for websites where updates to the database happen rarely (less often than every page loaded).
edit: I just realized that I may not have been fair to SQLite - I didn't index any columns in the SQLite database when I was serving it from a web page. This partially caused the slowdown I was experiencing. However, the observation of database-locking stands - if you have particularly onerous updates, SQLite performance won't match MySQL or Postgres.
another edit: Since I posted this almost 3 months ago I've had the opportunity to closely examine the scalability of SQLite, and with a few tricks it can be quite scalable. As I mentioned in my first edit, database indexes dramatically reduce query time, but this is more of a general observation about databases than it is about SQLite. However, there is another trick you can use to speed up SQLite: transactions. Whenever you have to do multiple database writes, put them inside a transaction. Instead of writing to (and locking) the file each and every time a write query is issued, the write will only happen once when the transaction completes.
The site that I mention I released in the first paragraph has been switched back to SQLite, and it's running quite smoothly once I tuned my code in a few places.
* the site is no longer available