Liquid mutation results from a preceding liquid r, l. This is a rather speculative mutation, based only on a couple of examples and what we know about Sindarin’s phonetic history. The only examples of liquid mutation appear in a couple of phrases from a document referred to as the Túrin Wrapper (VT50/5):

• ar·phent Rían Tuor·na: man agorech? “*and said (pent) Rían to Tuor: what have we done?”.
• sí il chem en i Naugrim en ir Ellath thor den ammen “*now all hands (cam-plural) of the Dwarves and Elves will be against us”.

In both phrases, Tolkien first wrote unmutated forms pent and cem before deleting them and replacing them with mutated phent and chem. These changes are consistent with the historical sound changes whereby voiceless stops become voiceless spirants after liquids and voiced stops became voiced spirants after liquids. Thus the main phonological result of liquid mutation is to turn stops into spirants. In the case of g, this spirant would ultimately be lost as it was in soft mutation. Probably initial h would “mutate” to ch because the sound change whereby initial [x-] became [h-] was inhibited, and likewise other voiceless sounds (hw, lh, rh) would be voiced.

Outside of the Turin’s wrapper, however, there is considerable evidence that liquid mutation was not a feature of modern Sindarin, and that the spirantalization of stops after liquids was no longer an active sound change in the language. In the King’s Letter there are a couple of uses of the conjugation ar “and” where no liquid mutation occurs (SD/128):

• ar Hîr i Mbair Annui “and Lord of the Westlands”, not mutated **ar chîr.
• ar Baravorn “and Hamfast”, not mutated **ar Varavorn.

This sound change is seen in some ancient names like Barthan “World-artificer” = bâr + tân, Erchamion “One-handed” = er + cam, Belthil “Divine Radiance” = bal + til. But there are a number of later compounds that show soft mutation instead, such as:

• calardan “lampwright” = calar + tan (PE17/96; RC/523).
• ithildin “moon-star” = Ithil + tin (LotR/317; PE17/66).
• Tegilbor “Calligrapher, *Pen-fist” = tegil + paur (PM/318).
• Tharbad “Crossway” = thar + pad (LotR/274; PE17/34).

Also, consider the following quote from the Quendi and Eldar essay discussing the plurals of compounds:

As a pronoun, usually enclitic, the form pen, mutated ben, survived. A few compounds survived, such as rochben “rider” (m. or f.), orodben “a mountaineer” or “one living in the mountains”, arphen “a noble”. Their plurals were made by i-affection, originally carried through the word: as rœchbin, œrydbin, erphin, but the normal form of the first element was often restored when the nature of the composition remained evident: as rochbin, but always erphin.

This quote indicates that i-affection of plurals only applies to the second element of recognized compounds (rochben → rochbin) but i-affection applies to the entire word when the compound was no longer recognized (arphen → erphin). If liquid mutation remained an active sound change in Sindarin, it would be hard to explain how arphen was not recognized as a compound.

Nevertheless, liquid mutation has remained a popular feature of Neo-Sindarin ever since it was first proposed by David Salo in his book, A Gateway to Sindarin (GS/78-79). Most Neo-Sindarin mutation charts include it, and there is some evidence (Turin’s Wrapper) that Tolkien at least considered it. It is also possible that it is an archaic mutation that has fallen out of use once the relevant sound changes ceased to be active in Sindarin, possibly as early as the arrival of the Noldor in Beleriand in the First Age, but almost certainly by the Second and Third Ages.

Summary: I would rate liquid mutation as a “very optional” mutation for purposes of Neo-Sindarin, since the evidence that Tolkien used it is limited to a single source (the Túrin Wrapper) and there is considerable evidence against it elsewhere. If you do use it, here is a summary of its probable effects:

• Initial voiceless stops (p, t, c) become voiceless spirants (ph, th, ch).
• Initial voiced stops (b, d, g) become voiced spirants (v, dh) or are lost: g → ’.
• Initial nasalized voiced stops ([m]b, [n]d, [n]g) do not mutate (remain b, d, g).
• Voiceless sounds (hw, lh, rh) are voiced to ’w, ’l, ’r.
• h becomes ch.

The l, r in the preceding preposition is not modified in any way.