The simplest approach is to just replace libcxx/test/lit.cfg.py with the lit.cfg.py file below, then you can just run the tests in-place via a command like:
$LLVM_SOURCE_ROOT/llvm/utils/lit/lit.py -s -i -j4 std/utilities/ratio
Alternatively, put the libstdcxx.cfg.in file in libcxx/test/configs/libstdcxx.cfg.in. Then, configure the LLVM tree with -DLIBCXX_TEST_CONFIG=<path-to-libstdcxx.cfg.in>.
Then, you should be able to use ./build/bin/llvm-lit -sv <whatever>.