If the verification logic is non-trivial, it will be messy to write a large lambda method (as your example shows). You could put all the test statements in a separate method, but I don't like to do this because it disrupts the flow of reading the test code.
Another option is to use a callback on the Setup call to store the value that was passed into the mocked method, and then write standard Assert
methods to validate it. For example:
// Arrange
MyObject saveObject;
mock.Setup(c => c.Method(It.IsAny<int>(), It.IsAny<MyObject>()))
.Callback<int, MyObject>((i, obj) => saveObject = obj)
.Returns("xyzzy");
// Act
// ...
// Assert
// Verify Method was called once only
mock.Verify(c => c.Method(It.IsAny<int>(), It.IsAny<MyObject>()), Times.Once());
// Assert about saveObject
Assert.That(saveObject.TheProperty, Is.EqualTo(2));