Tolkien often discussed this sound change in the context of how nasal-spirant combinations became long (voiceless) nasals, but the development of lth [lθ] was a special case:

Medially lþ, mph, nþ, ŋχ (though for long without change of spelling) became long voiceless l, m, n, ŋ, English transcription lh, mh, nh, ngh. In late Beleriandic Sindarin these became voiced ll, mm (m), nn, ng (= ŋg) unless followed still by a stressed syllable (phonetic notes from 1962, PE17/131).

Medially however nth (nþ), nch (ñx), mf (mp with bilabial f) and lth (lþ) became long voiceless n, ñ, m, l though the old spelling was mostly retained (beside nh, ñh, mh, lh), and among those to whom Sindarin became a language of lore, as were the men of Gondor who were or claimed to be of the Númenórean race, the spirant was reintroduced from the spelling. In true Sindarin of the Elves or Elf-friends of the early ages the final form was often reintroduced medially. In the transcription of Elvish Sindarin in The Lord of the Rings, ll is used as in the manner of modern Welsh for medial voiceless l; as in mallorn < malhorn < malþorn < malt “gold” and orn “tree” (The Rivers and Beacon-hills of Gondor, 1967-69, VT42/27).

There are some notes in Tolkien’s description of the Noldorin use of the Feanorian Alphabet that indicate Tolkien was already considering this sound change in the late 1930s:

Since in late Exilic and Toleressean medial lth j3 became voiceless ll; medial lh from l + h (s) is often written unhistorically j3 (Feanorian Alphabet, 1930s, PE22/32).

However, examples in The Etymologies from the mid-1930s (mostly written before the Feanorian Alphabet document) consistently show medial lth was preserved: N. toltho “fetch” (Ety/TUL); N. nelthil “triangle” (Ety/NEL, TIL); N. pelthaes “pivot” (Ety/PEL, TAK); N. malthen “of gold” (Ety/SMAL). The last of these may be contrasted with S. mallen “golden” in Cormallen “Golden Circle” (LotR/948; RC/625). The “canonical” example of lth > lh > ll is mallorn “golden tree”, and Tolkien described the sound changes of this word in several places:

• OS. malþorn > malhorn > S. mallorn (VT42/27), from the quote above.
• malt + orn > malh-orn > S. mallorn (PE17/50).
• ✶maltornē > malthorn > malhorn (PE23/140).

The word mallorn did not appear in The Etymologies, but it did appear in Lord of the Rings drafts from the 1940s (TI/226, 233), so likely Tolkien introduced this sound change between writing The Etymologies and starting work on The Lord of the Rings.

It is unclear whether or not ll should be voiceless or not in mallorn. The quote above from 1962 says that ll was later revoiced, but the quote from the late 1960s says that “In the transcription of Elvish Sindarin in The Lord of the Rings, ll is used as in the manner of modern Welsh for medial voiceless l” (VT42/27). This statement is quite sweeping, and implies that all double-l in Sindarin are voiceless. However, as Carl Hostetter pointed out (VT42/31, note #70) this is contradicted by Tolkien’s pronunciation notes in The Lord of the Rings appendices: “consonants written twice, as tt, ll, ss, nn, represent long, ‘double’ consonants” (LotR/1115), with no mention of voicelessness. At a bare minimum ll of other origins, such as in S. mellon “friend”, were almost certainly not voiceless, and it is possible that ll in mallorn was also regularized back to a voiced combination.

Furthermore, despite clearly describing this change in several places, Tolkien does not seem to have fully adopted the lth > ll phonetic development, even in the Sindarin period. There are quite a few examples of medial lth from names appearing in the 1950s and 1960s: S. Belthil, S. Belthronding, S. Brilthor, S. Gilthoniel, S. Melthinorn. These names can be explained as archaic forms (they all date to the First Age), but another interesting example, S. tolthui, appears as an alternate form of tollui “eighth” in The Rivers and Beacon-hills of Gondor notes quoted above:

The forms canthui, enchui, tolthui are those of the southern Sindarin dialect adopted by the Noldor (VT42/27).

The form tolthui is contrasted with its “normal” form tollui (VT42/25), but that normal form itself was first written as (deleted) tolthui (VT42/31, note #63). Tolkien’s vacillation is understandable in the context of two other statements from the same document: “the spirant was reintroduced from the spelling” and “the final form was often reintroduced medially” (VT42/27, from the quote above). It seems that in some circumstances the sound lth was restored, either drawing from tengwar spelling (j3), or by analogy from similar words ending in final -lt. Differing pronunciations may have persisted as dialectical variations, as with tollui vs. tolthui.

As a final item on ll, in notes on the Common Eldarin Article (CEA) from 1969 Tolkien said that the voiceless lh was pronounced as a single consonant rather than a double:

This simplification of long (“double”) consonants was not actually confined to final position. In the spoken language they were reduced initially and medially after an unstressed vowel followed by the main word-stress. The long consonants in Sindarin were mm, nn, ññ; ss; ll, rr; and voiceless llh (< ls, lþ). The simplification was, however, only normally recognized in spelling: initially (where it was always a product of mutation); and in the case of mm and llh. These had apparently become simplified to m, lh in all positions, and the double spelling was only retained to mark the position of the word-stress, where this still fell on the preceding vowel because the syllable had been closed by the double consonant: as remen “netted, entwined”, < *rembinā, beside galað-remmin (pl.) “tree-entangled”; malhorn, earlier malþorn (malt-ornē) “gold-tree”, beside uimallhen “ever-golden” (< oio-maltinā). The latter case was rare, because unnecessary: lh whether long or short in pronunciation was always derived from two consonants (PE23/140).

Thus voiceless ll behaved like mm, written llh (tengwar: mm) in cases where stress would matter, but always pronounced as a single consonant [l̥] or [ɬ], written lh (tengwa: m).

Conceptual Developments: As noted above, lth was preserved in The Etymologies from around 1937, and there are plenty of examples of lth in Gnomish and Early Noldorin of the 1910s and 1920s, so likely this sound change was introduced only towards the end of the 1930s. In Noldorin of the 1920s, voiceless lh could appear medially in compounds, but only when the second element already began with lh.

Neo-Sindarin: A number of Neo-Sindarin writers propose that Noldorin forms showing lth should be updated to ll to reflect the Sindarin phonetic rules described here. I personally think the lth and ll pronunciations can coexist in Neo-Sindarin as dialectical variations. In the entries in this lexicon, I consistently use the lth unless recording late Sindarin forms as written by Tolkien; this may even reflect the Sindarin tengwar spelling (see above). It is relatively straightforward to change lth to ll for those who prefer that pronunciation. The reverse transformation would be much trickier, since you would need to know which ll should not be changed back, such as in S. mellon “friend”.

If you do use the ll pronunciation from lth, I recommend sticking to voiceless [ɬɬ] or [ɬ] (as in Welsh) to keep it distinct from voiced [ll] of other origins.