[l]

[PVER•PVERVM•AMAT]

What sort of sounds can [l] come from?

[Grunnen]

What sort of sounds can [l] come from?

You'd probably be safe deriving it from a rhotic, [n], [d] (maybe not too likely), or, obviously [ɬ] (though I think having this sound implies having [l] already). I reckon [ð] would work. But others probably have some examples to back their claims up, and I don't, so...

[vec]

I think [n] and [d] are most common, but fricatives are possible as well [z] or [ð] for example, especially to "balance" out an asymmetric fricative system. Say a language has [f s x] and [v z ð ɣ] – [ð] would be likely to be lost. [l] is one possibility, or [ɹ], or [l] via [ɹ].

[Zaarin]

...[ɬ] (though I think having this sound implies having [l] already)...

Tlingit has /ɬ/ and several other laterals but no lateral approximants.

[Grunnen]

...[ɬ] (though I think having this sound implies having [l] already)...

Tlingit has /ɬ/ and several other laterals but no lateral approximants.

Wel, then this would work in at least one natlang. Wikipedia suggests [l] is present in that language as an allophone of /n/ in the speech of some older speakers though.

[Ziz]

After losing [l] altogether, Persian regenerated it in native words from clusters [rd] and [rθ] (cf. Old Persian θard- > New Persian sāl). Your best bet is probably some sort of change from [r] or [d] or clusters involving them, although cross-linguistically [l] > [r] is probably a lot more common than [r] to [l]. Also, don't forget that borrowing from other languages is a good way to (re)-introduce new phonemes.

[vokzhen]

In languages with a single liquid that varies between central and lateral, it seems that it's most l-like around /u o/, and most r-like around /i e/. I'm less sure of this, but I also vaguely recall r-like sounds are more likely around close vowels and l-like around open vowels. Of course those statements come into conflict with /u/, and I don't know if it's because different languages only take one or the other into account, or if I merely misremembered.

[linguoboy]

I reckon [ð] would work. But others probably have some examples to back their claims up, and I don't, so...

Modern Osage [l] derives from historical clusters of /xð/ and /kð/. (Osage /ð/ continues proto-Siouan *r, but LaFlesche actually transcribed these clusters as xth and gth when he did his fieldwork in the 1930s.)

Sino-Korean loanwords show the development /t/ > [l] in coda position, presumably via an intermediate *ɾ.

[vokzhen]

There's a number of Formosan languages where voiced alveolars may be lateral. Wikipedia only has information on a few of them, but Amis has [ð ~ ɮ] and Tsou has [ɗ ~ ˀl]. Sanskrit had [ɭ ɭʰ] as intervocal allophones of /ɖ ɖʱ/ that I'm pretty sure continued down into the present in some daughters.