I proof read a letter for a friend today. The body of the letter explained various situations over a 2 day period that made her uneasy. In her closing she wrote "I know this has been a very lengthy accounting of what took place over only two days" - it doesn’t SOUND right to me, I feel that it should say "a lengthy account of what took place".... I could very well be wrong but just would like to know! Thanks!
From Merriam-Webster, the third sense of accounting is:
3 : ACCOUNT 2 They were required to provide a detailed accounting of their actions.
what accounting can you give for your bizarre actions on the night in question?
The second sense of account that is referenced is:
a statement explaining one's conduct
This sense of accounting is essentially synonymous with account.
So, the use is not wrong—even though it is less common.
Yes, it is not correct technically.
Although her intended meaning is pretty clear, your "a lengthy account" is the best version. She could have said "...a very lengthy recounting of what took place...", to emphasize her feelings that her story or the way she told it was too drawn out.
"...a lengthy account..." might simply emphasize that since a lot has occurred, the story is simply going to be a long one if it is going to cover all of the relevant details.
A "very lengthy accounting" would require itemized spreadsheets with number amounts, which is clearly not the intended meaning here.