Let alone someone or something means something very different than let someone or something alone (also stated more commonly as leave something alone).
Let alone means to say nothing of/not to mention, and is used especially to emphasize the improbability of a contrasting example (the someone or something in the above example). let alone is used as an inseparable pair.
I can't remember the title of the book we were supposed to read, let alone the details of the story.
We haven't got the money to stay in a seedy motel, let alone a stay at the Ritz.
Synonyms for let alone are also word-pairs (or more): much less, never mind, still less, not to mention. These should also be kept together.
Let (x) alone means to avoid touching, bothering, or communicating with someone or something (such as interrupting).
Now therefore let me alone, that my wrath may burn hot against them and I may consume them, in order that I may make a great nation of you.
If those gentlemen would let me alone I should be much obliged to them.
If you get the impression that let (someone) alone is a more formal usage, it's because it's been replaced in more modern language by leave (x) alone.