The lldb tree contains a symlink directory, lldb/test/API/testcases, which points to the tests in ../../packages/Python/lldbsuite/test. Because the add_lit_testsuites() cmake rule does not follow symlinks, it doesn't find the nested directory tree to create make/ninja rules for.
Also, because the lldb lit config points the source root directly into the testcases tree, the check-lldb-api-testcases rule fails to find the testcases directory, and therefore finds no tests. Changing the source root to the containing lit file, like most lit configs do, fixes this.
After this patch, ninja check-lldb-api-testcases-linux works, and runs only the test cases in lldb/packages/Python/lldbsuite/test/linux.