Richard deserves his own post, I think.
They could have dressed him up as anything for this Halloween snapshot but they chose a dead guy with sunken eyes. Betelgeuse could have serenaded Lydia with any of the hundreds of great love ballads yet he chose not just one, but two songs sung by men named Richard.
Richard embodies the characteristics of both of Lydia's absentee parents. His death mirrors Charles' in its humorous and chaotic nature yet isn't framed that way within the plot. Charles' was a complete joke but Richard's is taken very seriously. He could have died any number of ways, but he died a watery aquatic predator death. In a film about death, it's too big of a coincidence.
As well, he was gone from Lydia's life long before he died, much like her mother. That his body was never found also forced us to briefly question whether or not he even was dead, just like we have with Lydia's mom for the past thirty years.
He serves no obvious purpose in the plot but to heal Astrid's trauma, and let's be real. The audience doesn't care about Astrid's trauma. We care about Lydia's. The argument could be made that he exists to mend the rift between Astrid and Lydia, but we don't need him for that. Jeremy accomplishes that all on his own.
Following the dreamverse, if we look at Astrid as a Lydia-proxy and Richard as a creation of Betelgeuse's, a "gift" of sorts, he suddenly makes all the sense in the world. Betelgeuse abandons Lydia in the afterlife (an inexplicably out-of-character choice outside of this context considering his three decades of pining) solely to allow her this healing reconciliation with Richard, the joint personification of her neglectful parents.
Richard saves Lydia (and more significantly, Astrid) because her real father never did.
Her real father sold her to Betelgeuse for a handful of snakes.