...Does the # 1666 in my serial number mean that it was the 1666th Lightening produced in 1968?
In this case the 1566th A65. BSA almost always started a new model year at 101 and subsequent years at 1001 or 3001 or 100001.
Even if say your 1666 was the last one built in '68 they would usually start at 2001 the following year. Makes it difficult to count how many models were built in a given year unless you had access to the build books.
"..you had access to the build books."
Which I did when I researched the original books in the UK in 2010.
Lightning number 1666 is the 1,566 A65/A50 machine built for the '68 model year regardless of which model, likely about September or October 1967. It is not the 1,666 Lightning built. Generally, but not always, the machines were built in model groups, sometimes in large quantities, sometimes in small quantities, throughout the model year. This applies to the 1965 thru 1968 model years for which I researched.
The exception was the 1967 model year which involved the "Y" machines. Those machines are at the end of the '67 model year in the books and on the inside front cover of the last model year book, as well after some blank pages in the last book. Enough said about that in this thread.
I cannot report on the singles, as I did not research those. Almost two days on the twins. By the end of the second day, my head was about to explode from information overload on this pea brain.