] ] Yes, Sir William Lucas was a knight.

] ..to deduce what order of knighthood he might have been awarded?

] If we assume he didn't rate the Garter or the Thistle, and the Guelfic Order wasn't available at the time of printing of P&P, does that mean he was a Knight of the Order of the Bath by default?

Marks - most knights were knights bachelor (or perhaps knights banneret, if that type still existed). That means they were simply knighted, without belonging to any chivalric order.

Being a knight of a chivalric order was considerably more socially prestigious, and getting the Garter was hardest - confined usually to Dukes (this century and the previous one being the height of aristocratic dominance in British politics) and to the odd untitled Prime Minister.

As for the public profile of knights, most knights today and then were obscure civil servants and politicians (known within a limited sphere). Today, more City knights exist i.e. businessmen who are knighted, along with the sports and entertainment knights.

In the Regency period, being knighted for sports accomplishments was pretty much unthinkable, and an actor could forget about being knighted. [It was not until much later - late Victorian and Edwardian that the odd great actor or manager was to be knighted, ditto for composers, conductors, and artists].

Consider this - Hogarth, Turner, Gainsborough, Constable etc etc were not knighted. But their counterparts today (of lesser skill IMHO) are usually knighted or receive decorations.

As for Sir William Lucas's knighthood, we are told from what it proceeded. Basically, he made a nice speech about the king and his ministers, and he was rewarded for this. [I am not sure if Jane Austen was writing tongue-in-cheek when she wrote that, or whether the government gave out knighthoods that readily. Either Sir William - NOT Sir Lucas - was very fortunate, or the government must have been really beset by critics and eager to reward the slightest praise].

In Chapter V of volume I, she says:
"WITHIN a short walk of Longbourn lived a family with whom the Bennets were particularly intimate. Sir William Lucas had been formerly in trade in Meryton, where he had made a tolerable fortune and risen to the honour of knighthood by an address to the King during his mayoralty. "

My own suspicion is that many mayors of important towns and cities were usually knighted, if they did not blot their copybooks. At one point, the practice was to make the Lord Mayor of London a baronet (higher-ranking, and hereditary). Some of these families then rose into the peerage. Mayors of important cities also founded notable families (one being the Bonham-Carters, descended from a Mayor of Bristol if I have my history right). See this link for information about past Lord Mayors of London who were knighted (a steady stream post-1660 to 1729, and occasional knights thereafter).
http://www.lordmayorsshow.org/hist/pastmayors.shtml

Assuming that Meryton was a mid-sized town (if not bigger), many mayors of Meryton could have risen to the knighthood over time. Not all, but some.

If any one wants to discuss this subject in detail,

--- Some links about knighthood --

Information about the Order of the Bath in the link and here:
http://www.royal.gov.uk/faq/honour8.htm

Information about knighthood in general
http://www.royal.gov.uk/faq/honour2.htm

On British honours for musicians
http://www.heraldica.org/topics/famous/knighthd
First British musician to be knighted was Bishop (1842)
Some musicians have turned down knighthood.

on writers (British and otherwise) honoured with a court of arms (or already possessing one)
http://www.heraldica.org/topics/famous/writers.htm
* this site mentions our own JA and this site *

And about the honour system today
http://www.royal.gov.uk/faq/honour.htm

I realize that these pages are of limited help in ascertaining how Sir William Lucas was knighted. But they are better than nothing, and they come from the monarchy's official site. As for the way in which offices, titles and peerages (in particular) were used to reward or gain loyalty by George III and the Prince Regent, any good book on the honours system, on 18th century British politics, or a good biography of either man should provide more information.