痛みのバラ

I wouldn’t know of any official statement regarding it. 

We do know, from HTR13, that L was a character whose design changed a lot over the course of the production (having been planned as a cool guy before Obata asked to make him eccentric, having no bags under his eyes in first design scribbles and such) so I assume that his design just shifted when drawing to whatever feels natural to Obata.

I don’t think they disappear during Yotsuba Arc, do they? If I’m missing a cap point me towards it, but I think his eyebrows go missing the first time literally a few pages into his introduction chapter and don’t appear at all past Vol 2.

From the very first page he appears, his eyebrows aren’t consistently present (check chapter 11 if you want to), but they’re at least moostly present until:

L on page 7 of chapter 11 (with eyebrows):

L on page 8, the very next page, of the same chapter (without eyebrows):

They very briefly reappear in chapter 14 on page 2:

They stay existent for the cover of chapter 15, but are nowhere to be seen within the actual chapter. Past that point, I don’t think there is any other sighting of the guy’s eyebrows at all.

The pages where he has them are very few at the start of his canon full-face appearances, so I think this is something that can be accounted to Obata not yet having his design down in a way that was pleasing to him. (In-universe, this is of course free game for headcanons. There just isn’t a canon reason for the lack of brows - neither production-wise nor in character.)

As for Mello and Near…. Obata stated he designed them to resemble  L in some form - specifically L’s ‘dead eyes’ should be a common factor between the characters. It seems that L’s eyebrowlessnesss was included.

EDIT: Actually, I think this is the whole number of appearances of L’s brows: