diff --git a/thrust/testing/transform_iterator.cmake b/thrust/testing/transform_iterator.cmake
new file mode 100644
index 00000000000..e02e34f5870
--- /dev/null
+++ b/thrust/testing/transform_iterator.cmake
@@ -0,0 +1,12 @@
+target_compile_options(${test_target} PRIVATE $<$<COMPILE_LANG_AND_ID:CUDA,NVIDIA>: --extended-lambda>)
+
+# this check is actually not correct, because we must check the host compiler, not the CXX compiler.
+# We rely on that those are usually the same ;)
+if ("Clang" STREQUAL "${CMAKE_CXX_COMPILER_ID}" AND CMAKE_CXX_COMPILER_VERSION VERSION_GREATER_EQUAL 13)
+    # When clang >= 13 is used as host compiler, we get the following warning:
+    #   nvcc_internal_extended_lambda_implementation:312:22: error: definition of implicit copy constructor for '__nv_hdl_wrapper_t<false, true, false, __nv_dl_tag<void (*)(), &TestAddressStabilityLambda, 2>, int (const int &)>' is deprecated because it has a user-declared copy assignment operator [-Werror,-Wdeprecated-copy]
+    #   312 | __nv_hdl_wrapper_t & operator=(const __nv_hdl_wrapper_t &in) = delete;
+    #   |                      ^
+    # Let's suppress it until NVBug 4980157 is resolved.
+    target_compile_options(${test_target} PRIVATE $<$<COMPILE_LANG_AND_ID:CUDA,NVIDIA>: -Wno-deprecated-copy>)
+endif ()
diff --git a/thrust/testing/transform_iterator.cu b/thrust/testing/transform_iterator.cu
index 1c8cbb5b44f..fa65443574f 100644
--- a/thrust/testing/transform_iterator.cu
+++ b/thrust/testing/transform_iterator.cu
@@ -2,6 +2,7 @@
 #include <thrust/functional.h>
 #include <thrust/iterator/counting_iterator.h>
 #include <thrust/iterator/transform_iterator.h>
+#include <thrust/logical.h>
 #include <thrust/reduce.h>
 #include <thrust/sequence.h>
 
@@ -255,3 +256,17 @@ void TestTransformIteratorIdentity()
 }
 
 DECLARE_UNITTEST(TestTransformIteratorIdentity);
+
+// see also: https://github.com/NVIDIA/cccl/issues/3541
+template <class Vector>
+void TestTransformWithLambda()
+{
+  using T = typename Vector::value_type;
+  Vector A{1, 2, 3, 4, 5, 6, 7};
+  const auto result = thrust::any_of(A.begin(), A.end(), [] __host__ __device__(T v) {
+    return v < 4;
+  });
+  ASSERT_EQUAL(result, true);
+}
+
+DECLARE_INTEGRAL_VECTOR_UNITTEST(TestTransformWithLambda);
diff --git a/thrust/thrust/iterator/transform_iterator.h b/thrust/thrust/iterator/transform_iterator.h
index 736678bce12..63df5356214 100644
--- a/thrust/thrust/iterator/transform_iterator.h
+++ b/thrust/thrust/iterator/transform_iterator.h
@@ -47,6 +47,9 @@
 #include <thrust/iterator/iterator_facade.h>
 #include <thrust/iterator/iterator_traits.h>
 
+#include <cuda/std/__memory/construct_at.h>
+#include <cuda/std/type_traits>
+
 THRUST_NAMESPACE_BEGIN
 
 /*! \addtogroup iterators
@@ -238,7 +241,26 @@ class transform_iterator
       , m_f(other.functor())
   {}
 
-  transform_iterator& operator=(const transform_iterator&) = default;
+  _CCCL_HOST_DEVICE transform_iterator& operator=(transform_iterator const& other)
+  {
+    super_t::operator=(other);
+    if constexpr (_CCCL_TRAIT(::cuda::std::is_copy_assignable, AdaptableUnaryFunction))
+    {
+      m_f = other.m_f;
+    }
+    else if constexpr (_CCCL_TRAIT(::cuda::std::is_copy_constructible, AdaptableUnaryFunction))
+    {
+      ::cuda::std::__destroy_at(&m_f);
+      ::cuda::std::__construct_at(&m_f, other.m_f);
+    }
+    else
+    {
+      static_assert(_CCCL_TRAIT(::cuda::std::is_copy_constructible, AdaptableUnaryFunction),
+                    "Cannot use thrust::transform_iterator with a functor that is neither copy constructible nor "
+                    "copy assignable");
+    }
+    return *this;
+  }
 
   /*! This method returns a copy of this \p transform_iterator's \c AdaptableUnaryFunction.
    *  \return A copy of this \p transform_iterator's \c AdaptableUnaryFunction.