This was a standard feature of flat file databases in the early 90s. There were many products. They often had an ODBC driver, which provided a SQL front end. dBase .dbf files were often used for storage. The arcane file locking in Windows is intended for exactly this kind of application.
Apart from quality (!), SQLite's main advantage over these products is broad platform support. And continued existence.
We still have a multi user desktop application that uses the Borland database engine and dbf files over a windows file server. The BDE is no longer supported but it still works
Apart from quality (!), SQLite's main advantage over these products is broad platform support. And continued existence.