BUG: groupby with sort=False creates buggy MultiIndex

doc/source/whatsnew/v1.1.0.rst

@@ -215,6 +215,7 @@ MultiIndex
         # Common elements are now guaranteed to be ordered by the left side
         left.intersection(right, sort=False)
 
+- Bug in :meth:`MultiIndex.is_lexsorted` was returning incorrect results when the levels of the multiindex weren't monotonic (:issue:`32259`)
 -
 
 I/O

pandas/core/groupby/ops.py

@@ -299,9 +299,14 @@ def reconstructed_codes(self) -> List[np.ndarray]:
     def result_index(self) -> Index:
         if not self.compressed and len(self.groupings) == 1:
             return self.groupings[0].result_index.rename(self.names[0])
-
-        codes = self.reconstructed_codes
-        levels = [ping.result_index for ping in self.groupings]
+        codes = []
+        levels = []
+        for code, ping in zip(self.reconstructed_codes, self.groupings):
+            levels.append(ping.result_index)
+            if ping.result_index.is_monotonic:
+                codes.append(code)
+            else:
+                codes.append(algorithms.factorize(ping.grouper, sort=True)[0])
         result = MultiIndex(
             levels=levels, codes=codes, verify_integrity=False, names=self.names
         )

pandas/tests/groupby/test_groupby.py

@@ -2015,6 +2015,30 @@ def test_dup_labels_output_shape(groupby_func, idx):
     tm.assert_index_equal(result.columns, idx)
 
 
+def test_sort_false_multiindex_lexsorted():
+    # GH 32259
+    d = pd.to_datetime(
+        [
+            "2020-11-02",
+            "2019-01-02",
+            "2020-01-02",
+            "2020-02-04",
+            "2020-11-03",
+            "2019-11-03",
+            "2019-11-13",
+            "2019-11-13",
+        ]
+    )
+    a = np.arange(len(d))
+    b = np.random.rand(len(d))
+    df = pd.DataFrame({"d": d, "a": a, "b": b})
+    t = df.groupby(["d", "a"], sort=False).mean()
+    assert not t.index.is_lexsorted()
+
+    t = df.groupby(["d", "a"], sort=True).mean()
+    assert t.index.is_lexsorted()
+
+
 def test_groupby_crash_on_nunique(axis):
     # Fix following 30253
     df = pd.DataFrame({("A", "B"): [1, 2], ("A", "C"): [1, 3], ("D", "B"): [0, 0]})