Sure you can download the sqlite file at the start of a session and work on it locally in a temp directory with atomic writes - but in the end the user doesn't think they have "saved" until version N+1 of the file is actually on their network share.
If there are many client programs sending SQL to the same database over a network, then use a client/server database engine instead of SQLite. SQLite will work over a network filesystem, but because of the latency associated with most network filesystems, performance will not be great. Also, file locking logic is buggy in many network filesystem implementations (on both Unix and Windows). If file locking does not work correctly, two or more clients might try to modify the same part of the same database at the same time, resulting in corruption. Because this problem results from bugs in the underlying filesystem implementation, there is nothing SQLite can do to prevent it.
A good rule of thumb is to avoid using SQLite in situations where the same database will be accessed directly (without an intervening application server) and simultaneously from many computers over a network.
text from here : https://www.sqlite.org/whentouse.html