Prepared for burial. The phrase has also been used to mean 'show something in the best possible light'. There are also reports of its use as meaning 'to criticize or condemn', but I can't confirm that usage.

The allusion is clearly to the practice of strewing lavender or other strong smelling herbs near dead bodies to mask their smell. The term was preceded by the much earlier phrase 'laid up in lavender'. This refers to the storage of clothes etc. with lavender to keep them fresh and free from insect damage - a precursor to mothballs. The practise was referred to in Robert Greene's, A quip for an upstart courtier, 1592. The phrase first printed in A new dictionary of the terms ancient and modern of the canting crew, 1690:

"Layd-up-in Lavender, when any Cloaths or other Moveables are pawn'd or dipt for present Money."

Laid out in lavender may or may not have derived from that earlier phrase. Either way it is an American coinage and isn't widely used elsewhere. The earliest citation of it that I've found is from the New York newspaper The Syracuse Herald, May 1926, in a book review:

"Now here is a regular detective story. It begins with a dog fight and winds up with the whole family laid out in lavender." [i.e., dead]