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To go at a quick pace; without delay.
Lickety probably derives from the word lick, which can mean 'to move quickly.' However, the origins for this phrase are unclear, and there are several questions regarding it that don't have answers. Questions such as: Why was split added to the end of lickety? Why did someone say lickety in the first place? Is it just a silly way of saying lick? I have no idea!

Nevertheless, looking at history, this saying goes back at least as far as the mid 19th century. For example, the expression is written in the Adams Sentinel newspaper from 1847, where it reads:

"On we went, lickity-split, the harrycame blowed harder, the timbers began to creak, the sails split to
ribbons, some of the spars begun to snap and go by the board, and then all at once there was a
terrible cry, 'breakers ahead!'"

I'm not exactly sure what a 'harrycame' is, but looking at the newspaper, that's how it is spelt. Honestly, the writer probably meant to type hurricane, as that fits well with everything else he said.
* Oh no, I've slept in and my dentist appointment is in 20 minutes... I need to get out the door and into my car lickety-split or I'll be late!

Note: The origins for most common idioms cannot be said with a certainty. What's provided are theories that may be plausible to how a phrase originated, but not necessarily so.

In addition, quotes that contain a particular phrase may be taken from old newspapers, poems, or books that were written centuries ago, but this by no means confirms that the phrase originates from said newspapers, poems, or books. In all likelihood, if an expression is being used in a newspaper, it's probably already a well known saying and is from an older time.
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