I disagree with superpentil.
The question as you phrase it is two-parted:
a) does the second usage come from the first original one? b) has "long" a different meaning here?
Now, granted, superpentil responded only to the phrases you put forth. And in that limited sense, he tried to make an argument that they are both related to time. But I believe your question is about the two meanings, not simply the two phrase examples you cited.
The answer to b) is that, in fact, "long" does not actually have a meaning in the "provided that" definition. There is no actual meaning to the term "as long as" when it means "provided that;" the only meaning resides in the idiom itself.
Let's take a different example for the conditional usage. How about this sentence? "As long as you say 'Bob's your uncle,' I'll give you a present."
Is there a time component to the condition?
No, there is not. The recipient of the present can say 'Bob's your uncle' quickly, slowly, immediately or after a while, and in all cases, he would qualify to receive the present. Further, though it's implied that he say the phrase prior to receiving the present, technically he can say it either before or after he gets the gift.
By using this alternative example, it's clear (at me at least) that the phrase has nothing to do with time, in any way. This completely collapses superpentil's argument (again, out of respect to him, it's important to note that he made the argument about the specific example you posed).
Further, I can think of a million ways in which condition would have nothing to do with time…and I'm guessing you can as well. And since we can do that, it becomes obvious that the definition of "long" here is ONLY idiomatic.
However, in the first usage ("as long as you live"), the word "long" clearly has the meaning we associate it with--length. And in that idiom, the word "long" means just what we know it to mean: length of time. The same idiom could also be used to describe physical length ("Rapunzel had hair as long as the Tower of London").
The answer to a) appears to be more difficult, especially since you said you wanted an empirical source.
Both the Oxford Dictionary and the American Heritage Dictionary of Idioms indicate that the usage of the phrase which revolves around length of time dates back to the 1400s:
- For the period of time that, as in You may keep the book as long as you want, that is, keep it for whatever time you wish to. [Early 1400s]
However, the idiom referring to condition dates back to some 400 years later: 3. Also, so long as; just so. Provided that, as in As long as you don't expect it by tomorrow, I'll make the drawing, or So long as sales are greater than returns, the company will make a profit, or You may have another cookie, just so you don't take the last one. [Early 1800s]
I will continue to research and see whether I can find out more.
UPDATE: After another day of research, including talking to a former high-school English teacher of mine on Facebook, we found nothing further. I will fall back on the Oxford and American Heritage dictionary date citations, which indicate the terms were coined in vastly different eras; this would potentially explain why the word 'long' has no meaning in the conditional idiom, which was coined much later than the other.