I am running macOS Big Sur Version 11.1 on Silicon and still get the error about the missing lzma.h file. I can confirm that I use the latest Python 3.9.1 version which includes the patches of this issue.
gcc -Wno-unused-result -Wsign-compare -Wunreachable-code -DNDEBUG -g -fwrapv -O3 -Wall -std=c99 -Wextra -Wno-unused-result -Wno-unused-parameter -Wno-missing-field-initializers -Wstrict-prototypes -Werror=implicit-function-declaration -fvisibility=hidden -I./Include/internal -I./Include -I. -I/usr/local/include -I/Users/dev/Downloads/Python-3.9.1/Include -I/Users/dev/Downloads/Python-3.9.1 -c /Users/dev/Downloads/Python-3.9.1/Modules/_lzmamodule.c -o build/temp.macosx-11.1-arm64-3.9/Users/dev/Downloads/Python-3.9.1/Modules/_lzmamodule.o
/Users/dev/Downloads/Python-3.9.1/Modules/_lzmamodule.c:16:10: fatal error: 'lzma.h' file not found
#include <lzma.h>
Is this supposed to be still the case? Thank you!