It does need to be added to the Rules and Codex Supplement, I agree, and possibly errata'd just for clarity. However,
here is the ruling you are looking for where Laddinfance clarifies that your first solution is the correct one. Because of the trait, it gains 2 Life each upkeep and only 2 Life. It does not compound.
Now that we have the main question out of the way, you make several valid points that I'd like to discuss. First, it doesn't need to say the word "trait." Life +X is a trait regardless, just like Melee +X is always a trait. Now, since in this case we have a trait with a variable component to it, it is certainly a valid question as to whether you calculate that variable just at the time of casting or do you continue to update the variable each time it changes. With the confirmation from Laddinfance, we know that you are supposed to continuously update it each time the number of Crush tokens changes, but we don't really have rules for handling traits that behave this way currently.
I'm pretty much certain that the intention is not for Death Lock to eliminate the Life that has already been acquired, since Finite Life doesn't tend to negate previous increases to one's Life. However, it could be argued that changing the variable also applies a new time stamp to the trait, and thus Death Lock would cancel out the entire thing. We don't have any official word on this, but I would be very surprised if the previous gains went away.
So, assuming you can keep the previous gains to Life, what happens when the variable increases? Since the time stamp of the trait obviously isn't changed under this assumption, it is feasible that the Life gain bypasses the Finite Life trait. However, I'm pretty certain in this instance that they did not intend for it to bypass Finite Life like this. Which means that the changes to the variable would have their own time stamps separate from the trait itself.
Again, simply assuming this is the case because we have no official word, if we go with this then the typical way that Death Lock works in these situations, such as if you were to apply Bull Endurance after the Finite Life was applied, is that it suppresses the Life +X trait rather than countering it. This is because the trait is a constant effect rather than a one time effect (which would have resulted in the value always being 0 for Stranglevine if it was only one time). Thus, if Finite Life is removed, the creature would immediately gain all of the Life that was being denied to it all at once.
So, to recap, we have the following three possibilities:
1. Each time the variable changes, it applies a new time stamp to the trait resulting in Finite Life removing the entire thing and Stranglevine being reduced to only it's base Life.
2. Changes to the variable are able to ignore the Finite Life trait because they neither have nor change any time stamps.
3. Changes to the variable have their own time stamp separate from the Life +X trait, allowing Finite Life to prevent further increases to the trait but not negating the increases already acquired. This is what I believe to be correct, but only by making assumptions as to the designers intentions. All three are equally valid according to the official rules we currently have, as far as I know. As echephron stated, I too was not a playtester yet for this card.
