SQLite Forum

To read file simultaneously
The use of SQLite for a remote database file strongly discouraged. If, as you seem to say, only reads are done over the network, "read" connections are opened as read-only, and writes are always local, you probably won't corrupt the database file. The odds are much worse with respect to the remote readers seeing a coherent set of on-"disk" structures; the ACID guarantees that pertain to purely local connections may not be met in your scenario.

People wanting to achieve a similar effect as you intend have created wrappers over the SQLite library or other combinations which undertake to leverage the library and overcome the (legion) limitations of network filesystems. A web search on "distributed sqlite database" (with the quotes) will turn up many such systems. Unless you do not care about what results the readers obtain, using one of those would be safer.

There are also some wrappers which expose a set of local SQLite database connections over a network, in effect making a client/server arrangement. This also can be done with high assurance that, should the remote results arrive, they are correct. Similarly, they provide high assurance that, should remote modifications get to the server, they do so with ACID still in effect.