(I'm just going to work my way backwards though this thread, because it seems interesting)
I don't understand that.
Lets say someone loves sandwiches and someone hates them.
Person one says "Sandwiches are delicious." That is true for person one but false for person two.
That's not a lie, nor is it a truth (and the person saying it probably isn't saying it as a truth most of the time) it's just a opinion. Although sometimes clarifying a opinion as such (in situations where it could be mistaken as truth) can be usful, I am pretty sure it's not a necessary thing most of the time (And, indeed, in some cases people will feel insulted if you do so).
Although I guess I couldn't agree with the wording of "If it's not always true, then it's false." I can understand where it is coming from, if a statement is true, then it is true, and if it is false or a lie, then it is false or a lie. Although though the passage of time the answer to a question might become different, that doesn't change how true or false a statement on it was previously.
As for person saying the day of the week... Saying it's not always wrong or not always right is ignoring the context of the statement. The statement "It is tuesday" made on a tuesday is always right, and the statement "It is tuesday" made on a day other then tuesday is always wrong. I guess if you really want to devoid it of all context though, it would always be nether right nor wrong, since the statement doesn't clarify what 'it' is.
Well, no. A lie is by definition untrue. It literally cannot be true. That makes it not a lie.
Some truths are subjective.
No, this isn't true. If something is subjective, then it's not the truth. Or if it is the truth, then it's not subjective (although it may seem that way in some instances, like stating a opinion, but however you take a statement, it's ether subjective, and thus nether true nor false, or objective, and thus is true or false.)
Lies may become true isn't really right, although the sentiment behind it is fair enough. It might be pedantic to say it's incorrect, but it would also be correct to say so.
Also I guess the question the OP was answered already, so not much point getting too deep into that. I think I would have suggested not to tell him, if he was meh about it, and from what the lie is, it seemed like one of those... I wouldn't call it a harmless lie since it was somewhat insulting to your mother, but exaggeration between friends is fairly normal in my experience, and I would guess this was just that? It would depend on a lot of things, but in my experience at least those types of lies are only weird if you later say that you were lying, them just finding out that you were lying is par for the course. Hopefully not a big deal ether way.