"What purpose does the lightning bolt (Which represents 'Update Now' in Quicken) serve just to the left of the Payee in some of my register transactions?"
The way you have phrased that tends to muddy the waters of comprehension.
The lightning bolt is part of the Check# field, so it will only appear at all, if the Check# column is selected. And it will appear to the left of some other column, if the Payee column is not selected. Also, even if the Payee column is selected, the lightning bolt will appear to the left of the "Date" column if the Preference to "Show date before check number" is not selected.
And the lightning bolt you're asking about has nothing to do with "Update Now".
As thecreator noted, the lightning bolt is "an indicator" that the transaction containing the lightning bolt is an online billpay transaction.
I think the best information you can get about the lightning bolt is to click it. That will display the "Payment Status as of mm/dd/yy" for that online billpay transaction. And in the lower left of that "Payment Status ...." display is a blue circle with a question mark in the middle: click the blue circle to see what Help has to say.
The lightning bolt, is an indicator of an Online Payment / Check that you sent using Quicken and a Direct Connect Connection to either your Bank's Bill Pay or Quicken Bill Pay.
"Does it ever get totally cleared - or is it a fixed icon indicator of the transaction using online Bill Pay ?"
It's permanent. And clicking the lightning bolt always displays the "Payment Status".