diff --git a/.azure/gpu-tests.yml b/.azure/gpu-tests.yml
index 74c1df4553fe0..7e5af0ea6cfe6 100644
--- a/.azure/gpu-tests.yml
+++ b/.azure/gpu-tests.yml
@@ -73,7 +73,7 @@ jobs:
         CUDA_VERSION_MM=$(python -c "import torch ; print(''.join(map(str, torch.version.cuda.split('.')[:2])))")
         pip install "bagua-cuda$CUDA_VERSION_MM>=0.9.0"
         pip install -e .[strategies]
-        pip install deepspeed==0.6.4  # TODO: remove when docker images are upgraded
+        pip install deepspeed>0.6.4  # TODO: remove when docker images are upgraded
         pip install --requirement requirements/pytorch/devel.txt
         pip list
       env:
diff --git a/requirements/pytorch/strategies.txt b/requirements/pytorch/strategies.txt
index db29ce556e839..4eafac99b8c66 100644
--- a/requirements/pytorch/strategies.txt
+++ b/requirements/pytorch/strategies.txt
@@ -1,5 +1,5 @@
 fairscale>=0.4.5, <=0.4.6
-deepspeed>=0.6.0, <0.6.5
+deepspeed>=0.6.0, <0.7.0
 # no need to install with [pytorch] as pytorch is already installed
 horovod>=0.21.2, !=0.24.0, <0.25.1
 hivemind>=1.0.1, <=1.0.1; sys_platform == 'linux'
diff --git a/src/pytorch_lightning/lite/lite.py b/src/pytorch_lightning/lite/lite.py
index 981eed30635f6..5125bf4486a9d 100644
--- a/src/pytorch_lightning/lite/lite.py
+++ b/src/pytorch_lightning/lite/lite.py
@@ -40,6 +40,7 @@
     has_iterable_dataset,
 )
 from pytorch_lightning.utilities.exceptions import MisconfigurationException
+from pytorch_lightning.utilities.imports import _RequirementAvailable
 from pytorch_lightning.utilities.seed import seed_everything
 
 
@@ -105,6 +106,8 @@ def __init__(
         self._precision_plugin = self._strategy.precision_plugin
         self._models_setup: int = 0
 
+        self._check_deepspeed_support()
+
         # wrap the run method so we can inject setup logic or spawn processes for the user
         setattr(self, "run", partial(self._run_impl, self.run))
 
@@ -456,6 +459,18 @@ def _check_strategy_support(self, strategy: Optional[Union[str, Strategy]]) -> N
                 f" Choose one of {supported} or pass in a `Strategy` instance."
             )
 
+    def _check_deepspeed_support(self) -> None:
+        if (
+            isinstance(self._strategy, DeepSpeedStrategy)
+            and self._strategy.zero_stage_3
+            and _RequirementAvailable("deepspeed>=0.6.5")
+        ):
+            # https://github.com/microsoft/DeepSpeed/issues/2139
+            raise RuntimeError(
+                "DeepSpeed ZeRO-3 is not supported with this version of Lightning Lite and `deepspeed>=0.6.5`."
+                " Please downgrade deepspeed to 0.6.4 or check if a newer version of Lightning is available."
+            )
+
     @staticmethod
     def _supported_device_types() -> Sequence[_AcceleratorType]:
         return (
diff --git a/src/pytorch_lightning/utilities/deepspeed_model_summary.py b/src/pytorch_lightning/utilities/deepspeed_model_summary.py
index 89dd6a9f9a25f..45d55392df51d 100644
--- a/src/pytorch_lightning/utilities/deepspeed_model_summary.py
+++ b/src/pytorch_lightning/utilities/deepspeed_model_summary.py
@@ -17,7 +17,9 @@
 from typing import Dict, List, Tuple
 
 import torch
+from torch.nn import Parameter
 
+from pytorch_lightning.utilities.imports import _RequirementAvailable
 from pytorch_lightning.utilities.model_summary import (
     _is_lazy_weight_tensor,
     get_human_readable_count,
@@ -40,7 +42,11 @@ def num_parameters(self) -> int:
     @property
     def average_shard_parameters(self) -> int:
         """Returns the number of parameters in this module."""
-        return sum(p.partitioned_size() if not _is_lazy_weight_tensor(p) else 0 for p in self._module.parameters())
+
+        def partitioned_size(p: Parameter) -> int:
+            return p.partitioned_size() if _RequirementAvailable("deepspeed<0.6.6") else p.partition_numel()
+
+        return sum(partitioned_size(p) if not _is_lazy_weight_tensor(p) else 0 for p in self._module.parameters())
 
 
 class DeepSpeedSummary(ModelSummary):
diff --git a/tests/tests_pytorch/lite/test_lite.py b/tests/tests_pytorch/lite/test_lite.py
index 86a0a5a82195a..2215ab3129780 100644
--- a/tests/tests_pytorch/lite/test_lite.py
+++ b/tests/tests_pytorch/lite/test_lite.py
@@ -11,6 +11,7 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
+import contextlib
 import os
 from copy import deepcopy
 from unittest import mock
@@ -29,6 +30,7 @@
 from pytorch_lightning.strategies import DeepSpeedStrategy, Strategy
 from pytorch_lightning.utilities import _StrategyType
 from pytorch_lightning.utilities.exceptions import MisconfigurationException
+from pytorch_lightning.utilities.imports import _RequirementAvailable
 from pytorch_lightning.utilities.seed import pl_worker_init_function
 from tests_pytorch.helpers.runif import RunIf
 
@@ -478,4 +480,13 @@ def run(self):
             assert self.broadcast(True)
             assert self.is_global_zero == (self.local_rank == 0)
 
-    Lite(strategy=DeepSpeedStrategy(stage=3, logging_batch_size_per_gpu=1), devices=2, accelerator="gpu").run()
+    if _RequirementAvailable("deepspeed>=0.6.5"):
+        # https://github.com/microsoft/DeepSpeed/issues/2139
+        raise_if_deepspeed_incompatible = pytest.raises(
+            RuntimeError, match="DeepSpeed ZeRO-3 is not supported with this version of Lightning Lite"
+        )
+    else:
+        raise_if_deepspeed_incompatible = contextlib.suppress()
+
+    with raise_if_deepspeed_incompatible:
+        Lite(strategy=DeepSpeedStrategy(stage=3, logging_batch_size_per_gpu=1), devices=2, accelerator="gpu").run()