Bugfix/lightning nobin (#5349)

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**Context:**
The no-bin Lightning which derives from Device fails shots tests due to
the new condition.

**Description of the Change:**

**Benefits:**

**Possible Drawbacks:**

**Related GitHub Issues:**

pennylane/_qubit_device.py

@@ -280,17 +280,19 @@ def execute(self, circuit, **kwargs):
         sample_type = (SampleMP, CountsMP, ClassicalShadowMP, ShadowExpvalMP)
         if self.shots is not None or any(isinstance(m, sample_type) for m in circuit.measurements):
             # Lightning does not support apply(rotations) anymore, so we need to rotate here
+            # Lightning without binaries fallbacks to `QubitDevice`, and hence the _CPP_BINARY_AVAILABLE condition
             is_lightning = (
-                hasattr(self, "name") and isinstance(self.name, str) and "Lightning" in self.name
+                hasattr(self, "name")
+                and isinstance(self.name, str)
+                and "Lightning" in self.name
+                and getattr(self, "_CPP_BINARY_AVAILABLE", False)
             )
             diagonalizing_gates = self._get_diagonalizing_gates(circuit) if is_lightning else None
             if is_lightning and diagonalizing_gates:
-                self.apply_lightning(diagonalizing_gates)
+                self.apply(diagonalizing_gates)
             self._samples = self.generate_samples()
             if is_lightning and diagonalizing_gates:
-                self.apply_lightning(
-                    [qml.adjoint(g, lazy=False) for g in reversed(diagonalizing_gates)]
-                )
+                self.apply([qml.adjoint(g, lazy=False) for g in reversed(diagonalizing_gates)])
 
         # compute the required statistics
         if self._shot_vector is not None: