The new portrait of Justices O’Connor, Ginsburg, Sotomayor, and Kagan offers four views of the neck doily. Here is how Tony Mauro describes it:

A seated Justice Sandra Day O’Connor and Justice Sonia Sotomayor, seen standing behind her, look somber, while Justice Ruth Bader Ginsburg, seated next to O’Connor, and Justice Elena Kagan, standing next to Sotomayor, have faint smiles. They are wearing their black robes, with differing neckwear that accurately reflects their preferences.

O’Connor is wearing a sailor-suit neck doily. RBG is wearing the standard round teacup neck doily. Justice Sotomayor has no discernible neck accoutrement (not even the one RBG gave her). Justice Kagan rocks the subtle neck liner. Though she wore one at first, she soon stopped. She later said that she is not a frilly, lacy person.

Update: The Washington Post has a better photo of the painting. Justice Sotomayor is in fact wearing some kind of turtleneck neck doily.