Yes, see wikipedia:

https://en.wikipedia.org/wiki/Axolotl

That's what I was trying to reference, but I left the X in the English "Wax" [wax][alotl].

I am very curious what the author intended though

Not silent, but not either of the L sounds in English, /l/ as in lever and and /ɫ/ as in trouble. It's the ll in Welsh, /ɬ/ in IPA. If you pronounce it /t/ you'll be closer than /tɫ/, like bottle.

Fun fact, x is an sh sound because that's how it was in medieval Spanish around the time Spaniards got there and wrote down the words. Around this same time is when the Old Spanish sh sound was shifting to the value it has in the word México and later a spelling reform changed it to J or g before i and e (except eg. in a bunch of mexican place names which retrained old spelling)

I believe in other Iberian languages such as Portuguese, Catalan and Basque, the sh sound is spelled with X.

Axolotl are salamanders.