The reason that I ask is because this is happening to LiDAR, and I am inclined to use lidar because it is easier to read.
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As Wikipedia points out, probably the best rule of thumb is "can you speak it as a single word?". For instance, Nato (Nay-to) and Unicef (You-Ni-Cef), but USA (You-Ess-Ay) and FBI (Eff-Bee-Aye). Another common rule seems to be that anything less than five letters (NATO, FBI) can be capitalized all the way through, but anything longer than that (Unicef, Unesco) shouldn't, just because it looks ugly as full caps, although you can use small caps to make that look less ugly.
Personally, I think you should go with whatever your target audience is expecting.
I would assume acronyms lose their capitals once they become familiar and enter the English language as a standard word (laser, modem, ...)
Others won't be so quick to uses lowercase, like AIDS:
Several of the other answers use examples of acronyms that remain capitalized which aren't actually acronyms. Technically speaking, if you pronounce the individual letters of the term instead of phonetically abbreviating it into a word, it is an initialism.
That distinction is commonly accepted, and makes it clear that acronym is a hypernym of initialism. Many references list the reverse definition for acronyms, but the ordering always agrees that initialisms are primarily pronounced separately and acronyms are
Note that RaDAR and LiDAR are not initialisms as they both derive their first two letters from a single word. That makes them even more distinguished as acronyms; if they were purely initialisms, they would be RDR and LDR, respectively.
To the question at hand, the reason I mention this is to establish that the capitalization of the acronym does not relate to the capitalization; that is to say, capitalization is independent from the difference of initialism vs. acronym. Almost all initialisms are fully capitalized. Only when an abbreviation is a true acronym and pronounceable as a separate word does it appear to become eligible for alternate capitalization.
From the perspective of utility to the reader, the reason for this is obvious: initialisms must remain capitalized to signify that they are not regular words. Consider the following (terrible, contrived example):
Half of this sentence looks like a typographical mistake.
Capitalizing the initialisms signifies to the reader that these are not regular words. An experienced English speaker would instantly an a-phonetic, all-caps character grouping as an initialism, pronounce it as such and be able to locate a definition more easily (internet search engine capabilities notwithstanding). A new speaker of English would recognize the capitalization as well and at least would know that these are not regular words.
So what sets radar apart? To answer that, let's take a look at a recent acronym that's graduated from caps to lowercase acceptance: lol.
LOL stands for laugh(ing/ed) out loud. The OED traces LOL to 1989 and the jargon file from 1990 both list LOL as an all-caps initialism. In fact, the Oxford English Dictionary made headlines when it added LOL as an entry in 2011. You may not have noticed, but their entry includes a pronunciation key for the word and that includes a single word pronunciation in addition to the initialism pronunciation of el-oh-el.
It should be clear now that the chief driving force behind an initialization losing its capitalization and entering the vernacular is the same for every other ongoing change in language: repetition of us, scale of adoption, spread of familiarity.
As such, I would err on the side of caution and print "LiDAR": it will never be wrong and it's the most easily understood to identify an acronym. LiDAR is not that much newer of an invention that radar – radar is only 30 years older and LiDAR is now ~50 years old itself – so if it were a matter of age, it would have lost its capitalization by now. But then again, the 1935 patent application dubs the invention "Radiolocation" and makes no mention of "RaDAR".
Finally, this whole debate for this specific term is somewhat moot. Wikipedia has two citations for Lidar actually being a portmanteau of "light" and "radar" rather than an actual acronym itself. As such, its inventors intended it to be a common noun from the start, and therefore the lower case "lidar" is technically correct.
So what about acronyms that have entered the vernacular but remain capitalized? There are two classes of these.
First, as VonC covers, AIDS remains capitalized to distinguish the deadly disease from the mundane, pre-existing words. Similarly, WASP should be capitalized to distinguish white anglo-saxon protestants from flying stinging insects. Short acronyms are more likely to collide with existing words, simply because there are fewer possibilities and most of the pronounceable combinations are taken.
Second, there are organizations known by their acronyms remain capitalized because the acronym itself is a proper noun and rules of style dictate capitalization of the first letter to signify or respect their uniqueness and dignity. But as Guarav points out, sometimes acronym names are fully capitalized and sometimes they are only capitalized in their first letter. This turns out to be a matter of style as well. Abriding that gramarphobia article:
Finally, as names cross the boundary from language to law (in the form of copyright and trademarks), it can be necessary to bow to the desires of the named organization itself. UNICEF for example alternates between the all-caps and all-lowercase versions of their name on their website, seeming to prefer the former in text and the latter in their logo.
Similarly, Randall Munroe founded his non-acronym comic xkcd and defied common rules of language and phonics by decreeing that xkcd be capitalized like a word or like an acronym depending upon its place in a sentence.
This is of interest to me b/c I'm writing a manual for an ISO shipping container custom-built to house a LiDAR unit.
This article gives some good insight:
While totally subjective, it just feels "to soon" (in the life of the technology) to go the sonar, scuba and radar route. And there is one manufacturer spelling it "LiDAR."
However, since our customer seems to use Lidar the most (followed by LIDAR, but less than a as often as Lidar), that's likely the way I'll spell it.