diff --git a/docs/changelog/+missing-read-write-module.bugfix.rst b/docs/changelog/+missing-read-write-module.bugfix.rst
new file mode 100644
index 00000000..97701c08
--- /dev/null
+++ b/docs/changelog/+missing-read-write-module.bugfix.rst
@@ -0,0 +1,3 @@
+Resolving :class:`~filelock.ReadWriteLock` or :class:`~filelock.AsyncReadWriteLock` raises the :exc:`ImportError` when a
+module other than Python's :mod:`sqlite3` is missing, as in a frozen application that left out a filelock submodule. The
+names are ``None`` only without SQLite.
diff --git a/src/filelock/__init__.py b/src/filelock/__init__.py
index 15a6a55e..45332e7c 100644
--- a/src/filelock/__init__.py
+++ b/src/filelock/__init__.py
@@ -112,10 +112,13 @@ def __getattr__(name: str) -> object:
         raise AttributeError(msg)
     try:
         module = import_module(module_name, __name__)
-    except ImportError:  # pragma: lacks sqlite3
-        if module_name not in {"._read_write", "._async_read_write"}:
+    except ImportError as error:
+        # Only a missing sqlite3 module (the package, CPython's _sqlite3, PyPy's _sqlite3_cffi) leaves the read-write
+        # locks None; a frozen application that left out a filelock module gets the error that names it.
+        sqlite_missing = (error.name or "").startswith(("sqlite3", "_sqlite3"))
+        if module_name not in {"._read_write", "._async_read_write"} or not sqlite_missing:
             raise
-        value = None
+        value = None  # pragma: lacks sqlite3
     else:
         if name == "asyncio":
             value = module
diff --git a/tests/test_lazy_import.py b/tests/test_lazy_import.py
index c597ec1a..2988109d 100644
--- a/tests/test_lazy_import.py
+++ b/tests/test_lazy_import.py
@@ -65,6 +65,49 @@ def test_lazy_import_resolves_asyncio_submodule() -> None:
     assert _run("from filelock import asyncio; print(asyncio.__name__)") == "filelock.asyncio\n"
 
 
+def _hidden_module_script(blocked: str, missing: str, attribute: str) -> str:
+    return f"""
+        import sys
+        class Hide:
+            def find_spec(self, name, path=None, target=None):
+                if name == {blocked!r}:
+                    raise ModuleNotFoundError(name={missing!r})
+        sys.meta_path.insert(0, Hide())
+        import filelock
+        try:
+            value = getattr(filelock, {attribute!r})
+        except ImportError as error:
+            print(f"error:{{error.name}}")
+        else:
+            print("none" if value is None else "resolved")
+        """
+
+
+@pytest.mark.parametrize(
+    ("blocked", "missing", "attribute"),
+    [
+        pytest.param("sqlite3", "sqlite3", "ReadWriteLock", id="package"),
+        pytest.param("_sqlite3", "_sqlite3", "AsyncReadWriteLock", id="cpython-binding"),
+        pytest.param("_sqlite3", "_sqlite3_cffi", "ReadWriteLock", id="pypy-binding"),
+    ],
+)
+def test_lazy_import_missing_sqlite3_leaves_read_write_lock_none(blocked: str, missing: str, attribute: str) -> None:
+    # coverage loads sqlite3 before filelock, so only an unmeasured child can miss it
+    assert _run(_hidden_module_script(blocked, missing, attribute), measured=False) == "none\n"
+
+
+@pytest.mark.parametrize(
+    ("module", "attribute"),
+    [
+        pytest.param("filelock._read_write", "ReadWriteLock", id="sync-read-write"),
+        pytest.param("filelock._async_read_write", "AsyncReadWriteLock", id="async-read-write"),
+        pytest.param("filelock._soft", "SoftFileLock", id="other-lazy-module"),
+    ],
+)
+def test_lazy_import_missing_filelock_module_raises(module: str, attribute: str) -> None:
+    assert _run(_hidden_module_script(module, module, attribute)) == f"error:{module}\n"
+
+
 def test_lazy_import_async_file_lock_subclasses_file_lock() -> None:
     assert {filelock.FileLock, filelock.BaseAsyncFileLock} <= set(filelock.AsyncFileLock.__mro__)