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Plan for an 64 bit binary for macosx catalina?
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Same problem here - Catalina/64-bit/x86, and just today resolved for the current sqlite3 version, 3.35.5.  The key advice appears at https://sqlite.org/howtocompile.html, under item 3:

"Building shared libraries for Mac OS X and Windows is not nearly so simple, unfortunately. For those platforms it is best to use the configure script and makefile that is included with the TEA tarball."

As a Tcl fan, I understood "TEA tarball."

What worked for me:
1. Download the source code archive file, specifically having the .tar.gz file extension.

2. Extract from the archive, and build (configure + make), following instructions for sqlite3 in the README.txt file. 

3. Change directories to ./tea, and follow instructions in the TEA-specific README file. One output of this second build action in my case was a "libsqlite3.35.5.dylib" file.  Depending on your target directory, you may need to use "sudo make install."

FYI, Mac OSX now generates errors when loading imported .dylib files that are not certified. It's a new security feature.