Yes, I believe it is a voiceless allophone of a phoneme [ʎ] - soft/palatized [l] (ль). That's how we pronounce [ʎ]: https://seeingspeech.ac.uk/ipa-charts/?chart=1&datatype=3&speaker=1#location=654 . The tip and blade of your tongue contact the alveolar ridge and the hard palate anteriorly. However, in this context, there is a regressive (backward) assimilation: "st" makes "l" voiceless. We don't have voiceless [l] as a phoneme, that's why we don't distinguish them in a transcription. It seems close enough to this sound: https://seeingspeech.ac.uk/ipa-charts/?chart=1&datatype=3&speaker=1#location=106 . You just need to put your tongue in a [ʎ]-position and do not use your vocal cords. Good luck! upd: However, "ль" is voiceless here only when you pronounce it quickly. Actually, you don't have to learn how to pronounce it voiceless.

First, touch the part of your tongue behind its tip to the roof of your mouth (that should be the only part touching). Then try to pronounce the sounds L with a very brief Y following immediately after (zero time gap).

I guess it is less voiced than it usually is because of the subsequent "ST". My tongue is just in the same place where it is when I say "лес" or "лифт", but the sound is really short