If you used SQLite with SQLProvider in the recent past, just adding the System.Data.SQLite.Core NuGet package wasn’t enough. Due to SQLProvider wanting to access databases already during edit and compile time, you also had to copy subdirectories with System.Data.SQLite native interop DLLs for x64 and x86 to a certain directory. This operation had to be repeated when you updated or restored the NuGet package.
Starting with the just (yesterday) released System.Data.SQLite.Core Version 1.0.104, this is no longer needed. Joe Mistachkin, the package author, has added a configuration file especially for us F# type provider users. It allows the interop DLLs to be loaded during edit/compile time without prior copying (see this feature request for details). In short: to use SQLProvider with SQLite now, just add the System.Data.SQLite.Core NuGet package, and it will just work.
A big thanks to Joe Mistachkin for this F# type provider adaption!
(The SQLProvider documentation for SQLite will be updated to reflect this change.)