Reynardine's name (and his initial encounter with Annie) are inspired by the traditional song "Reynardine", which Anne covered.
Winsbury is from the traditional song "Willie O' Winsbury" (interestingly, Kate Rusby also recorded a variant of this song, titled "John Barbury"). In the song, Willie is in a relationship with the king's daughter, Janet, much to the king's displeasure. Replace "king" with "headmaster" and ... yeah.
Lindsey & Bud's names, and the fact that they're engineers in an underwater habitat, to The Abyss.
Tom called Lily "Cookie Monster" when he named her in a tweet. She also shares his color scheme and seemingly has toned-down mannerisms and speech patters of Cookie Monster. She might be also a reference to another Perky GothGenki Girl with much the same colour scheme, perpetual crazy smile and lack of inhibitions in the L.A.W.L.S. comic.
This page might be one to The Lord of the Rings: Sam unhesitatingly grabs Frodo's hand when he's in the "hospital" in front of all their friends (it was kind of a big deal while filming the movie) while Kat hesitates to hold Annie's hand despite (or perhaps because of) the only people around being Robot, Shadow 2, and Reynardine.
Chapter 48, "Tall Tales":
By coincidence (Tom doesn't plan what days comics are posted in advance) this calm meeting between a taller-than-average lady knight and a huge unwell misanthropic canine-themed warrior came just five days after this incredibly violent confrontation between a taller-than-average lady knight and a huge unwell misanthropic canine-themed warrior. Also present are the lady knight's shorter but talented male companion, a dangerous young girl who looks like her mother and acts like her father('s sister) that the canine-themed warrior "befriended", and the trickster who's manipulating them all (also just off stage is the psychotic woman who's going to kill everyone even remotely associated with those who killed her loved one(s)... wait that could be anyone; specifically it's the dead one with white hair and white skin who was left in/by the river who un-lives only for vengence).