So you know that fanon [1] thing where vampires can only sleep or rest if they're getting treated like the dead, be it in a coffin or tomb, or simply under a burial shroud?
Consider: Because intentional turning is something positive for vampires, and one that functions more as a rebirth and a welcoming into an inner circle or a community, it's common to make richly decorated coffins or richly embroidered burial shrouds for the new vampire to use in their turning sleep and thereafter when they need to rest.
It's celebratory, and a symbol of belonging and investment in the new fledgling. Something like a bridal gift, something like a baby blanket.
Louis embroiders Owen's with little vignettes of important points in their relationship: their meeting over the mill, the first time Owen came back (ostensibly to discuss it further), the first time Owen came back without the mill as an excuse. Meetings in the woods, particular trees under moonlight.
And finally, the day Louis asked Owen if he wanted to turn.
- I'm guessing derived either from Dracula's condition of needing his grave's soil in his coffin, or the folklore that inspired that