The phrase "a process that lasted" is correct and usable in written English.
It can be used to describe the duration of a particular process or event in a narrative or analytical context.
Example: "The project was challenging, and it was a process that lasted several months before we achieved our goals."
Alternatives: "a process that continued" or "a process that endured".
She started working on "Bare" in 2001, a process that lasted more than a year.
It, in turn, enlisted an architect to procure the permits for the restoration, a process that lasted several years.
But Biden asked Mitchell to join him in calling every Democrat at home, a process that lasted until after two in the morning.
Following a foreign ministers' meeting in Helsinki in July 1973, committees met in Geneva to draft an agreement, a process that lasted from September 1973 to July 1975.
In choosing the 100 we began with a much larger total of worthy books and then pared it down, a process that lasted many weeks and involved much good-natured dispute and the occasional sleepless night.
Using a wheeled contraption equipped with a mirror and a Fresnel lens, he burned an arcing, 366-foot line in the dried, cracked surface, a process that lasted from dawn to dusk.
State law says that on June 4, candidates for Congress and the Legislature can begin circulating nominating petitions to enter party primaries, a process that lasts six weeks.
The sentence in (16a) is not acceptable because "one of these days" is too vague about when the weight loss will happen, and losing weight is a process that lasts an indeterminate amount of time.
To build a new school, the government must decide its location, plan its construction and examine tenders, a process that lasts until June, when the rainy season sets in.
It's a process that lasts around one millisecond and occurs many times a second in a running engine.
Such blobs, astronomers believe, could only arise deep within the core of the blast from the flash fusion of silicon atoms into unstable atoms of nickel, a process that lasts a fraction of a second and requires temperatures of at least 5 billion degrees.
