About the 99-year lease from Wikipedia

A 99-year lease was, under historic common law, the longest possible term of a lease of real property. It is no longer the law in most common law jurisdictions today, yet 99-year leases continue to be common as a matter of business practice and conventional wisdom.
The law
Under the traditional common law doctrine, the 99-year term was not literal, but merely an arbitrary time span beyond the life expectancy of any possible lessee (user) or lessor (owner).
William Blackstone (1723–1780, of Commentaries on the Laws of England fame) states that a lease was formerly limited to 40 years, although much longer leases (for 300 years, or 1000 years) were in use by the time of Edward III. The 40-year limit was based on the text The Mirror of Justices (book 2, chapter 27).
In the law of several US states, a 99-year lease will always be the longest possible contract for realty by statute, but many states have enacted shorter terms and some allow infinite terms.[citation needed]
Due to the influence of the ideas of Henry George at the time the Australian Capital Territory (ACT) was established in the early 20th century, all land in the ACT is held under 99-year leases, the first of which expired in 2023.
The 99-year lease concept has been more common under civil law regimes when it comes to concessions of territory: most concessions last for 99 years.

Why was the duration of territorial contracts often 99 years
The origins of the 99-year lease are unknown but have been a matter of speculation for centuries. However, that figure had become commonplace in many countries by the eighteenth and nineteenth centuries. It is thus unsurprising that negotiated territorial contracts included “99 years” as a ‘default period’ in many cases.
The English jurist and politician, Lord Edward Coke wrote on the subject of the duration of leases under English common law in the sixteenth century. This can be found in the first part of his Institutes of the Laws of England in the section on the laws covering “Of tenant for years”.
Firstly, he observes that a lease had to have a fixed term. So, for example, one could not say that a lease was granted “for as long as he shall live”. Such a lease would be void under common law:
“… as if one makes a lease for so many years as we shall live, this is void in present for the uncertainty.”
Similarly, one could not just say “for three generations”. A lease had to specify a fixed term. He notes that in the past, leases had been granted:
“… for a hundred or a thousand years, &c …”
But that:
“… a lease for years, though it is for a thousand or more, which never are without suspicion of fraud; and they were the lesser valuable, for that at the common law they were subject unto, …”                                                                                                So, in Coke’s time, 1000-year leases apparently carried a suspicion of fraud under Common Law. From this was born the legal fiction of the 999-year (and 99-year) lease as being something materially different from a 1,000-year (and 100-year) lease. (Presumably under a legal argument along the lines of: “No, m’lud, this isn’t one of these dodgy 1000-year leases that the law frowns upon, it’s just a 999-year lease!”)
It’s worth remembering that leases at that time were usually much shorter (21 years is a figure often quoted by Coke), but contemporary records of leases for 99 years and 999 years are known.
It is thought that the 99-year lease was meant to represent “3 generations” and a 999-year lease was meant to be a “lease in perpetuity” without actually giving away title to the land.
This is further discussed by Stanley L. McMichael in his book Long Term Land Leaseholds: Including Ninety-Nine Year

In England, during the sixteenth century, it was common practice to make leases for a term of three lives or a period of 99 years. It is presumed to be upon the theory that the lease should last through three generations as it has been common practice to accept thirty-three years as the span of a single generation.
McMichael also cites Coke:
Lord Coke, who lived during the reign of Queen Elizabeth, in his writings on the subject of leases suggested that a lease for 1,000 years might on its face suggest fraud and it is thought that to avoid such a contingency the lessors of those early days set upon 999 years as the extreme limit for the life of a lease. Such leases, in any event, were made at that time.
As the Wikipedia article on the 99-year lease notes, the 99-year lease became the maximum allowable by statute in many states in the US. It also became a de facto standard under English common law.
So, while the origins of the 99-year lease are uncertain, it was a standard under English Common Law by the sixteenth century, and commonplace in many countries by the eighteenth and nineteenth centuries. It is thus unsurprising that negotiated territorial contracts included that as the ‘default period’ in many cases.