Formally Disproving Divine Command Theory

[Godscreated]

Let's say that I am in a situation where someone is about to die. I have the opportunity to save their life if I lie though, so I do. According to the Bible, lying is a sin and therefore I am "morally bad" if we say the Bible is 100% correct morally.

For those Christians who say that lying in this case would have been justified, then it logically follows that Divine Command Theory falls apart:

p: there exists an objective moral code
q: lying is always wrong

First, we assume two things: p and "if p, then q". From this it logically follows that q, because if p, then q. For those of you who say lying was morally right in this case, it means you're assuming ~q (i.e not q). Here we have a contradiction where you're wanting to say q & ~q, which means that our conclusion must be one of our premises (p, if p then q) in the negated form; either ~p or ~(if p then q) because that way we avoid the conditions needed for this contradiction to arise.

Surely the believer will want to salvage p meaning that we must negate "if p then q". So our conclusion is therefore "it is not the case that if there exists an objective moral code then lying is always wrong". The problem is that the Bible asserts that "if p then q" but we have concluded that ~"if p then q". A contradiction arises which means we are left with questioning the validity of p as being a true statement, unless you wish to avoid this conclusion by simply saying you wouldn't have saved the person's life by lying.

Is not saving the person's life morally wrong? Are we obligated to save someone's life. What if I just shot the offender, wouldn't that solve the problem, I did not have to lie and I did not murder because it would be deemed a defensive killing, right?
With all that said which is probably not much why don't you give us a description of the situation, this way we will have more ground to argue and can do away with the Ps and Qs of it all. In other words what was the lie you told?