Learn English – Where does “on one’s last legs” come from

According to World Wide Words, it originates from firemen doing speed competitions without carrying water.

The term run, more fully fire run, has for at least the past century been used by local fire departments in the USA for a call-out to the site of a fire. It was once common for fire departments or volunteer hose companies to give exhibitions of their prowess at carnivals or similar events. [...] These competitions had fairly standard rules, of which several examples appear in the press of this period, such as in the Olean Democrat of 2 August 1888: “Not less than fifteen or more than seventeen men to each company. Dry run, standing start, each team to be allowed one trial; cart to carry 350 feet of hose in 50 foot lengths ...”.

These reports show that a dry run in the jargon of the fire service at this period was one that didn’t involve the use of water, as opposed to a wet run that did. In some competitions there was a specific class for the latter, one of which was reported in the Salem Daily News for 6 July 1896: “The wet run was made by the Fulton hook and ladder company and the Deluge hose company. The run was made east in Main street to Fawcett’s store where the ladders were raised to the top of the building. The hose company attached [its] hose to a fire plug and ascending the ladder gave a fine exhibition.”

It’s clear that the idea of a dry run being a rehearsal would very readily follow from the jargon usage, though it first appears in print only much later.

The phrase "Let's roll" has been in use as early as 1908, but achieved a special connotation on September 11th, 2001, as they were Todd Beamer's final words before rushing the cockpit on United Airlines Flight 93.

Wikipedia cites a possible origin of the word from 1908:

The phrase may have its origins as early as 1908 in the cadence song now called "The Army Goes Rolling Along", which likely extended into tank usage.

The same Wikipedia page also provides several other uses of the phrase in pop culture, including the 1950 Hemingway novel Across the River and into the Trees and its use in 50s and 60s police television shows such as Adam-12 and (the original) Dragnet.