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According to Wikipedia, North and South Korean treat word-initial ㄹ in Sino-Korean vocabulary differently:

In South Korea, ㄹ is silent in initial position before /i/ and /j/, pronounced [n] before other vowels, and pronounced [ɾ] only in compound words after a vowel. The prohibition on word-initial r is called the "initial law" or dueum beopchik (두음법칙). Initial r is officially pronounced [ɾ] in North Korea.

"labour" (勞動) – North Korea: rodong (로동), South Korea: nodong (노동)

"history" (歷史) – North Korea: ryŏksa (력사), South Korea: yeoksa (역사)

When did this divergence happen? Did the distinction exist before partition (and if so, are Northern dialects more conservative in terms of phonology more generally)? Did the divergence happen after the partition (and if so, do older speakers in the South retain these initials)? Or was this a "spelling pronunciation" constructed by North rather than a sound change that affected the South (and if so, has lack of initial ㄹ been part of Korean since when Sino- vocab was first borrowed or a later development)?

(Note: This question is about historical sound change and not about what the current rules are in either dialect. I would also appreciate sources for answers.)

A series of phonological changes regarding word-initial /ㄴ/ and /ㄹ/ are known to have started around Seoul, and spreaded to other regions, as most sociolinguistic changes happen. The change was a very slow and steady one, recorded at least since the 15th century, shortly after the invention of Hangul, which much more properly records Korean phonology than any priviously used writing system. The progress continued through the 16th and 17th century, became pretty much of the current form, at least around Seoul, during the 18th and 19th century, while the change spreading to other regions in the Korean Peninsula in different paces.

To answer one of your sub-questions, the Sino-Korean vocabulary was affected by this phonological change later than native Korean vocabulary. The Sino-Korean words were initially borrowed with their word-initial ㄹ/ㄴ, and then the change in the Korean Langauge applied.

Since the early 20th century, the change was more or less over in teh south. A rule very close to the current southern standard regarding the word-initial rule was included in the Unified Rules of Hangul Spelling (한글 맞춤법 통일안) of 1933 by the Korean Language Society (조선어학회).

Yet it was not fully reflected in the written language until the mid 20th century. You can see the first President's name, Rhee Syngman, written as both as 이승만 and 리승만 in contemporary records, but he seems to consistently pronounce his own name /이승만/ without the initial consonant. (See links for presidential election posters of 이승만 and 리승만) He was born near Kaesong, which is close to Seoul both geologically and sociolinguistically.

The word-initial rule was definitely in progress also in the northern dialects, but not to a full level. I don't know much about the spoken language pre-partiton, but in this blog post you can see both "력량(力量)" and "영도자(領導者)", which the modern northern standard would write "력량" and "령도자". Both are apparently written between 1945-1948. (The flag of Taegukgi was abolished by the northern autorities in 1948.)

Then the northern authorities came with the Joseon Language Spelling Rules (조선어철자법) in 1954, overruling the word-initial rule of the previously de facto standard Unified Rules (1933). I'm not aware of any research on this particular choice, but maybe it's a result of a conservative linguitisic prescriptivism, or a deliberate choice to avoid allomorphy in written forms. In the modern Pyongyang dialect it seems the word-initial rule is more or less reverted even in the spoken language in a more retroactive way compared to the records of the 1930s and 1940s. I would say this is a case of the written standard affecting the spoken form (a "spelling pronunciation").

If you are available to Korean literature, some papers worthy of reading:

• 김영황 (2014). 력사적으로 본 한자음초성 《ᄂ, ᄅ》의 표기문제. 중국조선어문, 2014(1), 12-16.


• 성낙수 (1987). 이른바 한국어의 두음 법칙 연구. ≪한글≫ 197, 한글학회, 3-39.


• 신성철 (2018). ᄅ 두음법칙의 통시적 고찰. 국어학, 85, 151-179.


• 조규태 (2009). 낱말머리 “ᄅ” 표기의 바뀌어옴에 대하여. ≪배달말≫ 45, 배달말학회, 69-109.

김영황 (2014) is a view by a northern scholar, a professor of Kim Il-sung University, apologetically explaining why they should keep the word-initial consonants. The other three are written by southern scholars, in effort to merly report and explain the phonological phenomenon.

Disclaimer: I am just a student of Korean linguistics with no academic authority. Especially the translations of the Korean terms 한글 맞춤법 통일안, 조선어학회, and 조선어철자법 are by myself with no research on the academic tradition.