A smoking jacket is a man's comfortable upper body garment, typically made of velvet, designed to be worn while smoking a pipe or cigar after dinner. Lambert sings here of her desire for a nicotine addict who is, "Velvet and refined, he's defined to hold me."
Lambert wrote the song with regular collaborator Natalie Hemby and Lucie Silvas. The latter is a British singer-songwriter, who achieved two UK Top 10 singles in the mid-2000s ("What You're Made Of" and "Breathe In.") Silvas has been married to John Osborne of the Brothers Osborne since June 2015. She is also credited for backing vocals on The Weight of These Wings.
Phil Collins may have named his 1985 album No Jacket Required, but several other artists have written songs with the garment in the title. They include
Fall Out Boy's "The Kids Aren't Alright" song title is not a reference to The Offspring's 1998 single of the same name. It actually alludes to The Who's 1979 rockumentary film called The Kids Are Alright.