How can clock/and watch be credited to saving lives, saving livelihood, etc.?

Seriously?
Read Longitude by Dava Sobel.

I assume you are looking for hypothetical situations. Viola!

If there was one thing about Bill that everyone could agree on, it was his ability to carry a grudge larger than the load capacity of a Chevy Tahoe. And I don’t mean one of the newer Tahoes with fancy seating options and wimpy engines. No, I’m talking about an old, rusty Tahoe with the big V-8 and no third row seating: a real Tahoe!
On that day in homeroom Janet told him, once again, that she was not interested in being his lab partner, or any other kind of partner for that matter, leaving him odd man out in Biology class scheduled late in the day.
While his IQ was in the +2 sigma region it was clear his EQ was located just as far in the negative direction. He did not make friends and didn’t have a clue how to go about it. Was it his lack of a verbal filter, his poor athletic ability, his asymmetrical features akin to a sea sponge, or was it simply the puzzle piece “I’m an Aspy” shirt he insisted on wearing to school every day since his diagnosis in 9th grade?
He left school after first period English class and walked the 10 minutes home, steaming. He knew the house would be empty since both his parents were at their respective jobs hoping to earn enough so they could afford future health care and education expenses. “Greatest country in the world. Hah!”
Wandering into the basement he saw the old 12 ga Ithaca shotgun that his great-grandfather used for duck hunting. “I wonder if it still works”, he thought grabbing 3 paper wrapped shells. “We’ll see”.
With the barrel off, the device was easily concealable in his pants and could be just as easily reassembled in fewer than 8 seconds. That is all the time he would need to make them all pay for every insult, every slight, every rejection he suffered in class. As he marched back toward the school his rage increased to a level he had not known before.
Holding the now reassembled relic, he kicked in the door and burst into the Biology room, screaming “Nobody move! It’s my time to be boss!” The kids cowered in the back of the room waiting for death. Suddenly there was a crash of broken glass, metal bits, and springs bouncing across the floor. Having just caved his head in like a ripe melon, Janet was standing above his lifeless body holding the empty frame of the wall clock she had ripped off the wall after returning from her fourth visit to the bathroom that day. Wiping the blood spatter off her face she muttered under breath, “It really is time for me to get this UTI checked out.”

If one is lost in the wilderness, an analog watch can be used as a compass. Holding the watch horizontal, point the hour hand to the sun; halfway between the hour hand and 12 is the direction south.

(This is for Northern hemisphere outside of the tropics during standard time. Adjustments can be made for Day,Ishtar Savings Time.)

Time zones were invented by railroads to reduce the number of train wrecks. Before, nobody knew when a train was coming because it was the same time everywhere, which meant nobody was sure what time it was. So the railroads divided the country into four zones and conductors got high quallity pocket watches so that everybody would know when every train was due to arrive.

Well….two weeks after my son moved out, when he was 17, I suddenly realized all my battery operated, decorative and dead wall clocks were set to 4:20.
That’s probably why.

It was a bright cold day in April, and the clocks were striking thirteen.

https://en.wikipedia.org/wiki/Thirteenth_stroke_of_the_clock

There is an 18th-century London legend of a clock that struck thirteen times and saved a man’s life. The story goes in Great Britain that St Paul’s Cathedral clock on one occasion struck thirteen bongs of the bell at midnight, with the result of saving the life of a soldier accused of sleeping at his post. An obituary notice of a John Hatfield that appeared in the Public Advertiser a few days after his death states that a soldier in the time of William III and Mary II was tried by a court-martial on a charge of having fallen asleep when on duty upon the terrace at Windsor. It goes on to say that he categorically denied the charge against him. He swore as a proof of his having been awake at the time that he heard St Paul’s Cathedral clock strike thirteen, the truth of which was much doubted by the court because of the great distance. Affidavits were made by several persons verifying that the clock actually did strike thirteen instead of twelve, and the soldier was pardoned.[7][a]

There is a poem that alludes to this published in 1774 called A Trip to Windsor by Timothy Scribble:

The terrace walk we with surprise behold,
Of which the guides have oft the story told:
Hatfield, accused of sleeping on his post,
Heard Paul’s bell sounding, or his life had lost

This is for @LuckyGuy. I should have had it in the detail: ”...finding out the time by looking at the clock and not via anything to do with digital technology.”

…I mentioned @LuckyGuy because of the length of the response, (I feel bad) but it’s for almost everyone else as well.

Bingo! @Pinguidchance