You're right, after reading what you've stated I have presupposed too much. I've attempted to create a more general and open ended question. It's not the same question, however I am curious about your position.
Can there be a universal moral lens without the creation/existence of a universal culture/religion?
Yes, but it depends on how you define the question. That definition also may not be satisfactory to many people. I'm not a utilitarian, but I'll take utilitarian as an example of how morality can be objective.
If you have as your standard that in order to live a good life, you must act in a way which maximises the happiness, or preferences, or follows the rules which maximises the happiness around you, then given you have defined your standard, morality is objective. There is, objectively, for an omniscient being, certain actions which promote happiness more. It is like a scale. The difficulty is that humans don't know which actions promote happiness more - one of the chief criticisms of utilitarianism is that you would callous their fingers on the calculator in an attempt to ascertain which action maximised utility. Nevertheless, an objective answer clearly exists given you've set the standard.
This is analogous to the scale of values in economics which exists as a result of the economic problem: limited resources, unlimited wants, thus our wants are automatically scaled - in fact even if resources were unlimited, wants would still be scaled as we can only perform one action at a time. Morality is no different. We are asking how to live a good life, and we live by thinking and acting. Consequently, if we are to think and act a certain way based on X standard, and yet there are many ways of thinking and acting around us we have to make a choice, and this choice defines us as a moral person. It defines us because as I said earlier, objectively, certain actions promote happiness more (if that is our standard), and so if we selected to act in a way that promoted happiness most, surely we must be on the 'morally good' path, and contrarily to promote happiness least, the opposite must also be true. Logically as potential actions are near infinite, we are not going to always select the 'best' action, but we can be closer to it than not.
That is how I believe an objective morality if you like exists, as analogised to the scale of value in economics. Morality now doesn't seem so sexy, there is no cosmic law, no divine hand, no esoteric reasons. Now given what I have just said, this is why I personally find an aspect of virtue ethics, and eastern philosophy quite seductive. Because it attempts to give you guidelines on how to live your life, such that even if you cannot analyze every action in detail, you can at least act in accordance with a code, and how well that code assists you in selecting actions which maximise utility (if that is your standard) will determine how good a person you are. Thus, once you've established the standard, and accept that you need guidelines to help you, you must also interrogate those guidelines. Is honesty a virtue? How much honesty? Far more useful than the trolley problem imo, although that is actually becoming a real issue with driverless cars.
So to answer the no universal culture/religion, yes. Different people, like they have a different scale of values, will also have different 'utility scores' assigned to their actions. Action X, Y and Z may give Person A 3, 2 and 1 points respectively, whereas it might give Person B 1, 2 and 3 points respectively. This could be due to their religion. Yet, given this knowledge, which action you should take ought be clear, and you will be considered to live a morally good life based on what I have just said. There is objectivity to you: the principle is objective, its application is not, because each person is different, and so how can they be expected to act similarly?
To reiterate, I don't much like utilitarianism, but since most people know of it, hopefully you can see how an objective morality can exist given you've laid down a principle - the key feature is the uncertainty. We may very much want to live a good life, but we don't know the way to do that. Sometimes this can be because we accept different standards. Sometimes different guidelines. Often times though, making a choice is hard. As I said, all this only applies given you've established a standard. The mechanism by which you establish the need for a standard is still important IMO, as that can affect the standard and guidelines which you think fit to follow.
Culture is just one variable which you have to take into consideration when deciding which action is most appropriate. It's actually quite easy to integrate because you have knowledge of the culture. For example, if you're gay, don't kiss in Saudi Arabia - rocket science levels of morality aren't required for that - unless of course your standard/guideline is something like: be true to yourself. See how far that takes you.
