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. The distinction had perhaps been felt too strongly. It had given him a disgust to his business, and to his residence in a small market town; and, quitting them both, he had removed with his family to an house about a mile from Meryton, denominated from that period Lucas Lodge, where he could think with pleasure of his own importance, and, unshackled by business, occupy himself solely in being civil to all the world. For, though elated by his rank, it did not render him supercilious; on the contrary, he was all attention to everybody. By nature inoffensive, friendly, and obliging, his presentation at St. James's had made him courteous….
Chapter 5.

Over the years there has been much speculation on the boards about just how and where Sir William was knighted.

Though the text is not specific , I have come to the conclusion that he was knighted after he made his address to the king at St James’s Palace while attending a levee.

Here is an old post of mine detailing the role of Mayors in the 18th/early 19th century, which will give you some background information to this post.

I have now found an instance of a man being knighted after making one of these addresses to the King.

He was Richard Arkwright, who from very humble beginnings ( his parents were very poor, and his first trade was that of perruke maker) was an entrepreneur and became a major mill owner in Derbyshire, and is considered the father of the modern industrial factory system . It is safe to say that his inventions were, in fact a catalyst for the Industrial Revolution.

This is a portrait of him by Wright of Derby. This is actually a very important painting because it is one of the first portraits of an industrialist in Britain, and it is interesting to note that while some of the conventions of aristocratic portrait painting are included (for example, the folded drapery) Arkwright is shown sitting not with any noble emblem of his learning (a globe, or books, for example) but with the set of cotton-spinning rollers. This was the fundamental part of the machine, which made Arkwright fortune (which was vast): it is disputed as to whether he invented this machine himself, but what is not disputed ish is his success and wealth.

On 22 December 1786,12 the eve of his fifty-fourth birthday, Richard Arkwright was knighted on presenting a loyal address congratulating the King (George III') on his escape from assassination at the hand of Margaret Nicholson.

An account, and not a very kind or well spelt one IMHO, of the ceremony has come down from Wilhelmina Murray, who on 25 December 1786 wrote to her husband, Captain George Murray, RN, uncle to the Duke of Atholl, of her visit the previous Saturday to the house of Sir Joseph Banks in Soho Square, where she:

was much entertained at the scene they had had the Morning before, in the arrival of the Great Mr. Arkwright who came to Sir Josephs in a black wig, brown frock, woosted stockings & Boots to ask him to go with him to the levee when he was to present an address on Margaret Nicholson’s affair.

Sir Jos. too good natured to refuse agreed but asked him about his dress. Mr. Ark- proposed going as he was, for he was not afraid they were but Men and so was He, however it was agreed he should take off his boots & return with good shoes at the proper hour our friends had a hint he would be worth seeing so took care to be in the way, but were not a little surprised to see little fatty appear a beau with a smart powderd bag wig so tight that coming over his ears it made him deaf; a handsome striped sattin Waist coat & proper coat with a sword, which he held in his hand, all provided it is suposed by Mr. Dempster, to crown the scene .Sir Joseph carried off his Beau and Brought him back Sir Richard Arkwright.

What a pity You happened not to be there then as the scene was excellent, the little great Man had no idea of kneeling but crimpt himself up in a very odd posture which I suppose His Majesty took for an easy one so never took the trouble to bid him rise."

Her is a picture of Sir Joseph Banks who was a British explorer and naturalist who, as long-time president of the Royal Society, became known for his promotion of science, and was friends with Sir Richard.