There are several ways to connect to SQLite from VBA. The simplest way probably is to use the SQLite ODBC driver and connect via the ADODB library. At the same time, the VBA code can call dll routines directly. While the x64 version of the dll should be usable for this purpose as built, the x32 version must follow the STDCALL/WINAPI ABI calling convention.
The official SQLite binaries follow the CDECL convention, but Windows distribution includes a suitable (at least in theory) SQLite copy, winsqlite3.dll. Rene Nyffenegger published a basic winsqlite3.dll example, illustrating this approach. Alternatively, a C-based dll adapter can translate CDECL to STDCALL, making it possible to use the current official SQLite release. SQLiteForExcel developed a dll adapter for the official SQLite binaries, and its fork demonstrates a refactored version employing a VBA class.
The most flexible approach relies on a custom-built STDCALL version of the library. I could not produce a usable STDCALL build using the MinGW toolchain (I could build it but not load it), so I decided to use another SQLite-supported Windows toolchain, MSVC, for this purpose.
The sqlite_MSVC_Cpp_Build_Tools.ext.bat script, placed in an empty writable directory and executed from an MSVCx32 shell, builds a working SQLite x32/STDCALL. Initially, I could not load an ICU-enabled build in VBA6. It turned out that, for some reason, Windows failed to resolve and load ICU dependencies automatically. After I had added the LoadLibrary calls loading individual ICU libraries explicitly in order of dependency (icudtXX.dll, icuucXX.dll, icuinXX.dll, icuioXX.dll, icutuXX.dll, sqlite3.dll), sqlite3.dll loaded successfully. (I have automated the loading process in VBA in a separate project.) Curiously, the x64 version compiled with MinGW did not exhibit this dependency resolution issue; however, a more recently compiled version using a newer ICU library has also become affected.