diff --git a/compiler/lib/Conversion/MidLFHEGlobalParametrization/MidLFHEGlobalParametrization.cpp b/compiler/lib/Conversion/MidLFHEGlobalParametrization/MidLFHEGlobalParametrization.cpp
index ed5c1c1db..0d471aba0 100644
--- a/compiler/lib/Conversion/MidLFHEGlobalParametrization/MidLFHEGlobalParametrization.cpp
+++ b/compiler/lib/Conversion/MidLFHEGlobalParametrization/MidLFHEGlobalParametrization.cpp
@@ -129,6 +129,70 @@ private:
   mlir::zamalang::V0Parameter &v0Parameter;
 };
 
+struct MidLFHEApplyLookupTablePaddingPattern
+    : public mlir::OpRewritePattern<mlir::zamalang::MidLFHE::ApplyLookupTable> {
+  MidLFHEApplyLookupTablePaddingPattern(mlir::MLIRContext *context,
+                                        mlir::PatternBenefit benefit = 1)
+      : mlir::OpRewritePattern<mlir::zamalang::MidLFHE::ApplyLookupTable>(
+            context, benefit),
+        typeConverter(typeConverter), v0Parameter(v0Parameter) {}
+
+  mlir::LogicalResult
+  matchAndRewrite(mlir::zamalang::MidLFHE::ApplyLookupTable op,
+                  mlir::PatternRewriter &rewriter) const override {
+    auto glweInType = op.getOperandTypes()[0]
+                          .cast<mlir::zamalang::MidLFHE::GLWECipherTextType>();
+    auto tabulatedLambdaType =
+        op.l_cst().getType().cast<mlir::RankedTensorType>();
+    auto glweOutType =
+        op.getType().cast<mlir::zamalang::MidLFHE::GLWECipherTextType>();
+    auto expectedSize = 1 << glweInType.getP();
+    if (tabulatedLambdaType.getShape()[0] < expectedSize) {
+      auto constantOp =
+          mlir::dyn_cast_or_null<mlir::ConstantOp>(op.l_cst().getDefiningOp());
+      if (constantOp == nullptr) {
+        op.emitError() << "padding for non-constant operator is NYI";
+        return mlir::failure();
+      }
+      mlir::DenseIntElementsAttr denseVals =
+          constantOp->getAttrOfType<mlir::DenseIntElementsAttr>("value");
+      if (denseVals == nullptr) {
+        op.emitError() << "value should be dense";
+        return mlir::failure();
+      }
+      // Create the new constant dense op with padding
+      auto integerSize = 64;
+      llvm::SmallVector<llvm::APInt> rawNewDenseVals(
+          expectedSize, llvm::APInt(integerSize, 0));
+      for (auto i = 0; i < expectedSize; i++) {
+        rawNewDenseVals[i] = llvm::APInt(
+            integerSize,
+            denseVals.getFlatValue<llvm::APInt>(i % denseVals.size())
+                .getZExtValue());
+      }
+      auto newDenseValsType = mlir::RankedTensorType::get(
+          {expectedSize}, rewriter.getIntegerType(integerSize));
+      auto newDenseVals =
+          mlir::DenseIntElementsAttr::get(newDenseValsType, rawNewDenseVals);
+      auto newConstantOp =
+          rewriter.create<mlir::ConstantOp>(constantOp.getLoc(), newDenseVals);
+      // Replace the apply_lookup_table with the new constant
+      mlir::SmallVector<mlir::Type> newResultTypes{op.getType()};
+      llvm::SmallVector<mlir::Value> newOperands{op.ct(), newConstantOp};
+      llvm::ArrayRef<mlir::NamedAttribute> newAttrs = op->getAttrs();
+      rewriter.replaceOpWithNewOp<mlir::zamalang::MidLFHE::ApplyLookupTable>(
+          op, newResultTypes, newOperands, newAttrs);
+      return mlir::success();
+    }
+
+    return mlir::success();
+  };
+
+private:
+  mlir::TypeConverter &typeConverter;
+  mlir::zamalang::V0Parameter &v0Parameter;
+};
+
 template <typename Op>
 void populateWithMidLFHEOpTypeConversionPattern(
     mlir::RewritePatternSet &patterns, mlir::ConversionTarget &target,
@@ -160,6 +224,24 @@ void populateWithMidLFHEApplyLookupTableParametrizationPattern(
       });
 }
 
+void populateWithMidLFHEApplyLookupTablePaddingPattern(
+    mlir::RewritePatternSet &patterns, mlir::ConversionTarget &target) {
+  patterns.add<MidLFHEApplyLookupTablePaddingPattern>(patterns.getContext());
+  target.addLegalOp<mlir::ConstantOp>();
+  target.addDynamicallyLegalOp<mlir::zamalang::MidLFHE::ApplyLookupTable>(
+      [&](mlir::zamalang::MidLFHE::ApplyLookupTable op) {
+        auto glweInType =
+            op.getOperandTypes()[0]
+                .cast<mlir::zamalang::MidLFHE::GLWECipherTextType>();
+        auto tabulatedLambdaType =
+            op.getOperandTypes()[1].cast<mlir::RankedTensorType>();
+        auto glweOutType =
+            op.getType().cast<mlir::zamalang::MidLFHE::GLWECipherTextType>();
+
+        return tabulatedLambdaType.getShape()[0] == 1 << glweInType.getP();
+      });
+}
+
 /// Populate the RewritePatternSet with all patterns that rewrite LowLFHE
 /// operators to the corresponding function call to the `Concrete C API`.
 void populateWithMidLFHEOpTypeConversionPatterns(
@@ -183,31 +265,47 @@ void populateWithMidLFHEOpTypeConversionPatterns(
 void MidLFHEGlobalParametrizationPass::runOnOperation() {
   auto op = this->getOperation();
 
-  mlir::ConversionTarget target(getContext());
   MidLFHEGlobalParametrizationTypeConverter converter(fheContext);
 
-  // Make sure that no ops from `MidLFHE` remain after the lowering
-  target.addIllegalDialect<mlir::zamalang::MidLFHE::MidLFHEDialect>();
+  // Parametrize
+  {
+    mlir::ConversionTarget target(getContext());
+    mlir::OwningRewritePatternList patterns(&getContext());
 
-  // Make sure func has legal signature
-  target.addDynamicallyLegalOp<mlir::FuncOp>([&](mlir::FuncOp funcOp) {
-    return converter.isSignatureLegal(funcOp.getType()) &&
-           converter.isLegal(&funcOp.getBody());
-  });
-  // Add all patterns required to lower all ops from `MidLFHE` to
-  // `LowLFHE`
-  mlir::OwningRewritePatternList patterns(&getContext());
-  populateWithMidLFHEOpTypeConversionPatterns(patterns, target, converter,
-                                              fheContext.parameter);
-  patterns.add<LinalgGenericTypeConverterPattern<
-      MidLFHEGlobalParametrizationTypeConverter>>(&getContext(), converter);
-  mlir::zamalang::populateWithTensorTypeConverterPatterns(patterns, target,
-                                                          converter);
-  mlir::populateFuncOpTypeConversionPattern(patterns, converter);
+    // function signature
+    target.addDynamicallyLegalOp<mlir::FuncOp>([&](mlir::FuncOp funcOp) {
+      return converter.isSignatureLegal(funcOp.getType()) &&
+             converter.isLegal(&funcOp.getBody());
+    });
+    mlir::populateFuncOpTypeConversionPattern(patterns, converter);
 
-  // Apply conversion
-  if (mlir::applyPartialConversion(op, target, std::move(patterns)).failed()) {
-    this->signalPassFailure();
+    // Add all patterns to convert MidLFHE types
+    populateWithMidLFHEOpTypeConversionPatterns(patterns, target, converter,
+                                                fheContext.parameter);
+    patterns.add<LinalgGenericTypeConverterPattern<
+        MidLFHEGlobalParametrizationTypeConverter>>(&getContext(), converter);
+    mlir::zamalang::populateWithTensorTypeConverterPatterns(patterns, target,
+                                                            converter);
+
+    // Apply conversion
+    if (mlir::applyPartialConversion(op, target, std::move(patterns))
+            .failed()) {
+      this->signalPassFailure();
+    }
+  }
+
+  // Pad lookup table
+  {
+    mlir::ConversionTarget target(getContext());
+    mlir::OwningRewritePatternList patterns(&getContext());
+
+    populateWithMidLFHEApplyLookupTablePaddingPattern(patterns, target);
+
+    // Apply conversion
+    if (mlir::applyPartialConversion(op, target, std::move(patterns))
+            .failed()) {
+      this->signalPassFailure();
+    }
   }
 }
 
diff --git a/compiler/tests/unittest/end_to_end_jit_test.cc b/compiler/tests/unittest/end_to_end_jit_test.cc
index 92859c509..2100bee09 100644
--- a/compiler/tests/unittest/end_to_end_jit_test.cc
+++ b/compiler/tests/unittest/end_to_end_jit_test.cc
@@ -414,6 +414,23 @@ func @main(%arg0: tensor<4x!HLFHE.eint<7>>,
   ASSERT_EQ(res, 14);
 }
 
+TEST(CompileAndRunTLU, identity_func_5) {
+  mlir::zamalang::CompilerEngine engine;
+  auto mlirStr = R"XXX(
+func @main(%arg0: !HLFHE.eint<5>) -> !HLFHE.eint<5> {
+    %tlu = std.constant dense<[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]> : tensor<32xi64>
+    %1 = "HLFHE.apply_lookup_table"(%arg0, %tlu): (!HLFHE.eint<5>, tensor<32xi64>) -> (!HLFHE.eint<5>)
+    return %1: !HLFHE.eint<5>
+}
+)XXX";
+  ASSERT_FALSE(engine.compile(mlirStr));
+  uint64_t expected = 3;
+  auto maybeResult = engine.run({expected});
+  ASSERT_TRUE((bool)maybeResult);
+  uint64_t result = maybeResult.get();
+  ASSERT_EQ(result, expected);
+}
+
 TEST(CompileAndRunTLU, identity_func) {
   mlir::zamalang::CompilerEngine engine;
   auto mlirStr = R"XXX(