As @Haleth mentions, age and degree of independence matter here. That is, both your age and your sister’s (not that I’m asking) and your mutual degree of independence from your parents.
It sounds from your description like your sister lives independent of your parents, which would make it at least possible for her to lie for you. (Let’s not put a fine point on this: When you say that you had hoped she could “cover for you”, what you really mean is that she could “lie for you” and say that she knows where you are when she really doesn’t, or when she knows that you’re somewhere that would make your parents upset.)
And apparently you aren’t independent of your parents, because that’s why they might choose to call her to ask if she knows where you are.
So, my assumptions are that you still live with your parents and your sister doesn’t. If she supports the idea of you dating a boyfriend but doesn’t support the idea of lying about it, then at least you know where you stand with her. There’s no reason why you can’t introduce your boyfriend to her, but you cannot and should not expect her to lie to your parents about that.
The best way to change culture, assuming you want to do this, at least in your own family, is to do it somewhat openly. Maybe not in a rush, and maybe not too much at once, but plainly and clearly. You already know that your parents don’t “approve” of you having a relationship that they don’t know about, but only you can gauge what their reaction might be. Will they become upset – angry – and attempt to convince you that you’re doing a bad thing? Or will they throw you out of the house? Or will they attempt to kill you? (I’m realizing that there are very wide ranges of people’s response to what they consider cultural violations.)
If you’re prepared to take on the consequences of going against your parents’ wishes, then my advice would be to tell them, take the consequences – whatever they are – and be open, honest and clear with everyone. Asking people to lie for you, while it may be successful in the short run, doesn’t do anything to solve the cultural problem that you face, and it can put the liar in a very awkward ethical place.
If you’re not prepared to face the consequences of your parents’ disagreement with your choice for how to live your life, then I suggest that you’re really not old enough (or mature enough, or just not independent enough) to make that choice in a practical and realistic way. Making a choice to defy cultural norms when you can’t, as we say, “carry the weight of your choice” can put you in a dangerous position, because it makes you “a square peg in a round hole” (meaning “different in a way that needs to be ‘fixed’”), but still dependent on the people whose norms you are attempting to defy or change.
I can certainly understand your impatience to live your life according to your own lights – I was young once, too, and I recall that – and while I did things that I had to be sneaky about when I was younger, and hope that I never got caught – I would never have expected anyone to lie on my behalf, and to say that I was doing one thing while they didn’t even know for certain what I really was doing. So I would suggest that you thank your sister for her support, but you should not be upset that she won’t lie for you. She has her own reputation for honesty to uphold, too, and that has to last her for the rest of her life.