[I know you'll disagree with this Thomas T

, but I just wanted to explain what is perhaps my own weird way of viewing the world!

]
I was trying to make the point, albeit poorly as usual, that although Adam's is talking in generalities about royalty, usurpers, "lewd embraces", unearned rights, control over others and taking more than their fair share of resources, the specific king that all would actually be thinking of in America during the time of the American War of Independence would be George III. Therefore the meaning of "lewd embraces" is in the general context of the speech the same as any husband's lewd embraces, but in the context of this section of the speech about royalty and the paragraph quoted in the OP all being addressed would be directly thinking of George III who had become the main focus of animosity. Just under one month before Adam's speech, this strength of feeling against George III was vented in Bowling Green Park (New York), where the gilded statue of the king upon a horse in the style of a Roman emperor was torn down by African slaves as ordered by the Sons of Liberty after the Declaration of Independence had been read to Washington's troops. Therefore anti-George III sentiments would be simmering and boiling throughout the Thirteen Colonies at that time.
Bowling Green (New York City) - Wikipedia
Successful invader:
The Hanoverian's themselves were seen by some as usurpers and invaders. George I became king in 1714 after the last Stuart monarch Queen Anne died. This was because he was Protestant and only a Protestant could become monarch as they would also become head of the (Protestant) Church of England. However, many saw this as wrong since George I was only Queen Anne's second cousin. There were in fact over 50 Catholic candidates with a closer relationship to Queen Anne and some thought they had a better claim to the throne. Hence the Jacobite risings which had only ceased in 1746 with the defeat of Bonnie Prince Charlie at Culloden.
Whig politicians believed Parliament had the right to determine the succession, and bestow it on the nearest Protestant relative of the Queen, while many Tories were more inclined to believe in the hereditary right of the Catholic Stuarts, who were nearer relations. In 1710, George announced that he would succeed in Britain by hereditary right, as the right had been removed from the Stuarts, and he retained it. "This declaration was meant to scotch any Whig interpretation that parliament had given him the kingdom [and] ... convince the Tories that he was no usurper."[27]
George I of Great Britain - Wikipedia
Therefore George III could be seen by some to be the great-grandson of a usurper and "invader".
Lewd embraces:
"Lewd embraces", while not directly meaning only George III it would no doubt remind people of him. George could be seen to be the product of a successful "invader" where the crown had been passed on "generation to generation" through the Hannovarians down to him. Also, George's father, Frederick the Prince of Wales had had nine children and George and his wife Charlotte were particularly fertile. By August 1776 they had already had ten children and showed no signs of stopping. Indeed, I believe they went on to have fifteen children in total. As such a contemporary in America or Britain might well see him (and perhaps the Hanoverians) as being rather expert in "lewd embraces".
George III of the United Kingdom - Wikipedia
[For anyone interested there is the online Georgian Papers Programme launched by the Queen, which is a five-year project to digitise original documents and papers, as part of this the Georgian Papers Online website allows free access to these scans. It was started in 2015 and is "a partnership between the Royal Archives, the Royal Library and King’s College London. The Omohundro Institute of Early American History & Culture (OI) and William & Mary are also sharing in this work as primary partners for the US." It takes some digging down through the links but eventually you reach viewable pdfs of the original documents.
What is in the Catalogue? )