Your understanding of the meaning of "take something lying down" is more-or-less correct: the something must be some negative or insulting event or action that you could choose to fight back against. When you say that someone is "taking something lying down", you are criticising them for doing nothing in response to something that has happened to them — they are "lying down" when they should have jumped to their feet and reacted immediately!
So, with that understanding, let's look at your example (I don't understand your second example, so I'll concentrate on the first):
Don't take your money lying down.
Since your money isn't an event or action, and it isn't negative or insulting, this sentence doesn't make sense. Something has to happen. So, perhaps, this might be closer to what you mean:
Don't take the theft of your money lying down.
Someone stole your money! That's an event or action that's negative, that you could take some action about (go demand your money back; report a crime; secure the money you have left; etc.). That's an awkward sentence though, which is why we are much more likely to say "take that lying down" or "take it lying down", where the pronouns that and it refer to something obvious from context. So,
They stole your money! Don't take that lying down.
As for your question in comments below, a suitable idiom that might convey a similar meaning about an object might be to "take something for granted." If you say:
Don't take your money for granted.
or
Don't take your rights for granted.
you're encouraging your reader to consider the real value of the object, and protect it appropriately.
