SQLITE can be configured to gracefully handle simultaneous writes in most situations. What happens is that when one thread or process begins a write to the db, the file is locked. When the second write is attempted, and encounters the lock, it backs off for a short period before attempting the write again, until it succeeds or times out. The timeout is configurable, but otherwise all this happens without the application code having to do anything special except enabling the option, like this:
// set SQLite to wait and retry for up to 100ms if database locked
sqlite3_busy_timeout( db, 100 );
All this works very well and without any difficulty, except in two circumstances:
If an application does a great many writes, say a thousand inserts, all in one transaction, then the database will be locked up for a significant period and can cause problems for any other application attempting to write. The solution is to break up such large writes into seperate transactions, so other applications can get access to the database.
If the database is shared by different processes running on different machines, sharing a network mounted disk. Many operating systems have bugs in network mounted disks that making file locking unreliable. There is no answer to this. If you need to share a db on a network mounted disk, you need another database engine such as MySQL.
I do not have any experience with Firebird. I have used SQLITE in situations like this for many applications over several years.