Proof: Lum's eye shadow is makeup in the OG anime (and manga) too.
In Episode 35 of the OG anime (screenshot 1-3), you can clearly see that Lum didn't have makeup when she was a child. Of course, the same is true for the remake version of the story, which was Episode 15 of Season 1 (screenshot 4-8).
However, in Episode 53 (screenshot 9-11) and 101 (screenshot 12-13), which are bath-focused episodes, you can still see her with eyeshadow. This could just be an oversight from the anime staff, like when Sakura's lipstick disappeared and reappeared in different shots.
These types of continuity errors happen in anime to this day. Albeit this one is a bit more extreme, as it's for a whole episode. So Ig the anime team simply forgot about it. Unless you think she naturally got her eye shadow when she got older, like her horns.
This thing is even trickier in the manga. Although you can see Lum with various colors of eye shadows in the colored cover pages, in the actual black and white panels, it almost looks like she has none in pretty much everywhere. But I think since both adaptations showed Lum without makeup when she was a kid, I think it's safe to assume it's like that in the manga too. Especially since the remake went to great lengths to be as accurate to the source material as possible.
Pic 14 and 15 are from Chapter 59 in the manga, which is what Episode 35 of the OG and Episode 15 of the remake adapted. Pic 16 is the cover of Chapter 132, which is what Episode 53 of the OG anime adapted. Sorry that they're not in English. The site where I used to read UY in high quality was shut down not long ago.
Before anyone asks, this was a fun little thing to research about. And I liked revisiting the anime after a long time, even if it was briefly.