Is there any common usage of accepted convention of transcribing voiceless laryngealisation?

e.g. [lˠ] → [l̥ˠ] or [l̥ˣ]

Or would [ɫ̥ ɫ] be the preferred notation?

I'm not quite clear on what you're describing as laryngealization. As I've always used the term, "laryngealization" describes the addition of glottal fry ("creaky voice"), which is itself a kind of non-modal voicing. Likewise, it can't really be unvoiced.

Are you talking about a secondary velar articulation perhaps?

Hmm, now I'm getting confused as well :/

I am talking about what most English speakers would call a "dark l", according to wikipedia, a voiced velarised alveo... oh, now I get it.

I'm terribly sorry, the title of the topic was supposed to be "velarised", and the question is about voiceless "velarisation". Gee, do I feel silly!



So, for lambdic consonants there are 3-4 qualities: flap [ɽ̊ ɽ], approximant [l̥ l], velarised approximant [ɫ̥ ɫ](?), and possibly palatalised approximant [ʎ̥ ʎ](?).

Lambdic flap is the normal realisation.
Lambdic velarised approximant occurs next to [n t d s]
Lambdic palatalised approximant occurs following [i y ɛ œ]
Lambic plain approximant occurs initially and geminate

Thus you could analyse it as a phonemic /ɽ/ with an allophonic [l], with further secondary articulation (or allophones): velarisation [ɫ~lˠ] and palatalisation [ʎ~lʲ].

Should I use the discrete symbols [ɫ ʎ] or modifiers [lˠ lʲ]? I am especially curious because the lambdic can be voiceless as well as voiced. So would that mean that [l̥ˠ] would still be correct? The modifier doesn't indicate any voicing, only secondary articulation?

YES, I am once again delving quite a bit deeper than actually necessary, but that's going to happen now and again

Velarization describes a process of adding a secondary closure during articulation. The closure itself does not characterize voice, so you can use the diacritic with both voiced and voiceless consonants.

As for using a diacritic versus an independent graph, the convention is to use the graph if the form is the primary expression of a phoneme but the diacritic if you are trying to indicate the result of a secondary phonotactic process.