To answer this question specifically, yes lightning scales to large transactions through Pickhardt payments, but for long term storage of sums, lightning isn't appropriate (though still works). I regularly move 1Msat between my node and a specific peer with a direct channel all the time, and since its a direct channel it's literally free. Lightning is a liquidity network, and in being so, it makes sending payments quick once bitcoin has been set aside on-chain for a lightning channel but the only purpose of doing this would be to later break it up into smaller sums. If your intention is to recieve a large sum and hodl it, why would you put it on the lightning network unless it was already there? Another way of saying the same thing is, if you dont ever intend to spend some money, why would you transfer it from your savings account to your checking account? Lightning is the checking account and debit card of bitcoin, where onchain transfers are more like a savings account.

Your topic is curious indeed, that should "big money" like governments be allowed to operate in darkness. I think that I understand why you bring it up. Bitcoin was designed to address this problem, but not in such a blunt-force way you are familiar with. Rather bitcoin was designed to address the secret or opaque counterfeiting of people's energy and thus allowing many cabals of conspirators to manipulate the world through the inherent imperfect-knowledge problem present in the market of money and credit.

Banknotes, what we call fiat, are inherently inflationary. There are two kinds if inflation, short-term and long-term. The kind everyone feels in their pocketbooks is long-term inflation. The kind the banksters and econunists use against us is short-term inflation, and they dismiss this theft by saying their banknotes are "more elastic" and claim its necessary to "lower the demand for money to enhance economic activity".

These are the kinds of deals we need as a society to put to an end, both the ability for inflationary loan-defaults to happen, and the dark smoke-filled backroom under-the-table deals done between international indistrial chieftains, the monied rich and the subversive deep state tyrants who all collude to keep their grip on the throats of hard working godfearing families.

Bitcoin, being a grassroots response to this eternal struggle between the honest and dishonest puts an end to manipulation of our liquid assets through lending of fiat or monopolistic hoarding of mining rights of metals.

If you study anarchism, you may find there is a connection between the corruption of government and the "imbalanced scales" used in coinage. To take this intrinsic need for a trust relationship around securing weights and measures away from the government, also largely neuters government altogether.

Therefore a concern bbout large sum transfers or holdings on the blockchain may be misplaced, and the underlying problem you are trying to solve is tyranny of a government or of a powerful international business. The greater likelihood is neither would be possible, nor necessary, and simply wouldn't exist under a system of perfectly hard money.