Before I begin this brief post, I want to make it clear that spam and trolling are prohibited from this blog. If you're reading this, kilo papa, that applies to you. If you want your posts published, then you're going to have to change your behavior.
Speaking of publication, I don't check this blog every day. Sometimes it takes as long as a week before I check it and publish any comments. That's due to my busy schedule, and in almost all cases not due to trolling activity on the part of those who comment.
With that out of the way, let's take another look at the modest version of the LCA (and no, I'm not addressing possible worlds semantics, but temporal necessity and contingency):
1. Everything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause. (Premise)
2. If the universe has an explanation of its existence, that explanation is a timeless, changeless, immaterial, and very powerful external cause. (Premise)
3. The universe exists. (Premise)
4. Hence, the universe has an explanation of its existence. (From 1 and 3)
5. Therefore, the universe is explained by a timeless, changeless, immaterial, and very powerful external cause. (From 2 and 4)
The argument is logically valid, so if the skeptic wishes to reject the argument, then one or more of the premises must be rejected. Surely nobody - unless maybe a solipsist - would reject premise (3). The only remaining premises are (1) and (2). Going backwards, let's turn our attention to premise (2).
There are a number of objections the skeptic could throw at premise (2). First, there is the objection that the universe, while having an explanation of its existence, simply exists by a necessity of its own nature. This would mean that no external cause is needed. The problem with this objection is at least twofold. First, it is entirely conceivable for the universe to not exist. While inconceivability does not necessarily entail impossibility, it certainly does undermine the skeptic's alternative. Secondly, we now know through the amazing discoveries of physics and astronomy that the universe began to exist at the Big Bang, entailing a state of affairs in which no matter or energy existed. Of course, there are fringe hypotheses that attempt to get around this problem, but with virtually no success, as the Borde-Guth-Vilenkin theorem essentially put the nail in the coffin to any alternative explanation.
A second objection to premise (2) is that it commits the fallacy of composition: "Sure, every part of the universe has an explanation, but the universe as a whole doesn't need to." I've never been impressed by this objection for (you guessed it) at least two reasons. First, there is the conceivability mentioned above that the universe might not have existed. This required the universe to exist contingently, and not necessarily. Secondly, this objection has always struck me as saying: "Just because there is an explanation of every member of the Pittsburgh Steelers, that doesn't mean the Steelers as a whole have an explanation." Do I even need to explain what's wrong with this objection? In case I do, of course the Steelers as a whole require an explanation! :) Management is an external cause, for example. We could provide example after example that undermines the composition fallacy objection, but I think enough has been said.
Lastly, what about premise (1)? Personally, I don't think this premise is even need of defense. To reject the Principle of Sufficient Reason (PSR) would be to undermine all of science, in addition to commonsense and everyday experience. Nobody in their right mind (unless he were jesting) would say: "that elephant in the middle of the street just exists without any explanation whatsoever." I take this version of the PSR to be properly basic, and even confirmed by the senses.
Now, what about another objection. Yes, I'm talking about the "what's God explanation?" objection, something that is supposed to appear very profound, but is among the weakest of atheistic objections. The timeless, changeless, immaterial, and very powerful external cause in (5) - let's call it "God" for expedience-sake - does have an explanation, but would have to exist by a necessity of His own nature. If God had an external cause, then He would be neither timeless nor changeless, since causation involves the actualization of some potentiality (a change). Since the universe just is the sum total of all physical space, time, matter, and energy, it follows that God cannot be externally caused and must exist by necessity.
Now, I realize there are other objections to the LCA, but my point in this post is to illustrate that it cannot be simply dismissed by long-refuted arguments against it. Truth is, the LCA isn't even my go-to argument. I much rather prefer St. Thomas Aquinas's First, Third, and Fifth Ways (plus the argument from desire), but a Thomist need not hide inside some Thomistic bubble. I also like the fine-tuning argument, the kalam cosmological argument (KCA), the argument from reason, certain ontological arguments, the moral argument, and even some practical arguments.