diff --git a/doc/releases/changelog-dev.md b/doc/releases/changelog-dev.md
index 9fe50728861..6b99fcbe0c0 100644
--- a/doc/releases/changelog-dev.md
+++ b/doc/releases/changelog-dev.md
@@ -210,6 +210,9 @@
 * `qml.AmplitudeEmbedding` has better support for features using low precision integer data types.
 [(#5969)](https://github.com/PennyLaneAI/pennylane/pull/5969)
 
+* `qml.lie_closure` works with sums of Paulis.
+  [(#6023)](https://github.com/PennyLaneAI/pennylane/pull/6023)
+
 
 <h3>Contributors ✍️</h3>
 
@@ -226,6 +229,7 @@ Emiliano Godinez,
 Renke Huang,
 Josh Izaac,
 Soran Jahangiri,
+Korbinian Kottmann,
 Christina Lee,
 Austin Huang,
 William Maxwell,
diff --git a/pennylane/pauli/dla/lie_closure.py b/pennylane/pauli/dla/lie_closure.py
index 931befcfd4f..7ed9a939314 100644
--- a/pennylane/pauli/dla/lie_closure.py
+++ b/pennylane/pauli/dla/lie_closure.py
@@ -14,6 +14,7 @@
 """A function to compute the Lie closure of a set of operators"""
 # pylint: disable=too-many-arguments
 import itertools
+import warnings
 from collections.abc import Iterable
 from copy import copy
 from functools import reduce
@@ -135,8 +136,11 @@ def lie_closure(
     while (new_length > old_length) and (epoch < max_iterations):
         if verbose:
             print(f"epoch {epoch+1} of lie_closure, DLA size is {new_length}")
+
         for ps1, ps2 in itertools.combinations(vspace.basis, 2):
             com = ps1.commutator(ps2)
+            com.simplify()
+
             if len(com) == 0:  # skip because operators commute
                 continue
 
@@ -144,6 +148,7 @@ def lie_closure(
             # remove common factor 2 with Pauli commutators
             for pw, val in com.items():
                 com[pw] = val.imag / 2
+
             vspace.add(com, tol=tol)
 
         # Updated number of linearly independent PauliSentences from previous and current step
@@ -151,6 +156,9 @@ def lie_closure(
         new_length = len(vspace)
         epoch += 1
 
+        if epoch == max_iterations:
+            warnings.warn(f"reached the maximum number of iterations {max_iterations}", UserWarning)
+
     if verbose > 0:
         print(f"After {epoch} epochs, reached a DLA size of {new_length}")
 
diff --git a/tests/pauli/dla/test_lie_closure.py b/tests/pauli/dla/test_lie_closure.py
index fc2f4361e90..50babf8e000 100644
--- a/tests/pauli/dla/test_lie_closure.py
+++ b/tests/pauli/dla/test_lie_closure.py
@@ -344,7 +344,9 @@ def test_max_iterations(self, capsys):
             PauliSentence({PauliWord({i: "X", (i + 1) % n: "Z"}): 1.0}) for i in range(n - 1)
         ]
 
-        res = qml.pauli.lie_closure(generators, verbose=True, max_iterations=1)
+        with pytest.warns(UserWarning, match="reached the maximum number of iterations"):
+            res = qml.pauli.lie_closure(generators, verbose=True, max_iterations=1)
+
         captured = capsys.readouterr()
         assert (
             captured.out
@@ -501,6 +503,17 @@ def test_lie_closure_heisenberg_generators_even(self):
         res = qml.pauli.lie_closure(generators)
         assert len(res) == 4 * ((2 ** (n - 2)) ** 2 - 1)
 
+    @pytest.mark.parametrize("n, res", [(3, 4), (4, 12)])
+    def test_lie_closure_heisenberg(self, n, res):
+        """Test the resulting DLA from Heisenberg model with summed generators"""
+        genXX = [X(i) @ X(i + 1) for i in range(n - 1)]
+        genYY = [Y(i) @ Y(i + 1) for i in range(n - 1)]
+        genZZ = [Z(i) @ Z(i + 1) for i in range(n - 1)]
+
+        generators = [qml.sum(XX + YY + ZZ) for XX, YY, ZZ in zip(genXX, genYY, genZZ)]
+        g = qml.lie_closure(generators)
+        assert len(g) == res
+
     def test_universal_gate_set(self):
         """Test universal gate set"""
         n = 3