Unless you have statistics and facts to measure the level of “popularity” amongst the fandom and not just your subjective perceptions of what you see as popularity, I can’t take your post seriously. Again, the fandom is more than just your own little bubble.
While this might not be the most accurate, one possible measurement that we can use is Pixiv fanart. Since we can look at the number of fanart with tags for certain characters, we can see how much fanart each character has.
According to Pixiv, Mallow has just over 1300 pieces of fanart, Lana has just under 2300 pieces of fanart, and Lillie has just over 4600 pieces of fanart. Of course, these Pixiv tags may be applied to fanart which do not solely focus on said characters, but that does give a general idea as to how they each fare in popularity in Japan alone. One of the reasons that Mallow has much less fanart than the other two Pokegirls is that people don't really ship her with Ash; I found plenty of fanart shipping Ash with Lillie or Ash with Lana, but practically none for Ash with Mallow
On the other hand, if we use Danbooru as our source, we see that both Mallow and Lana have around 1100 pieces of fanart, while Lillie has around 3500 pieces of fanart.
In my opinion, Lillie's lead in fanart is likely due to her having a more major role in the games and manga, so I will try and see whether there's a separate tag for the Pokegirls in just the anime.
I'm not sure whether Danbooru is the most accurate source though since it is more of a conglomerate for fanart from different sources, a better source for gauging Western popularity of each character would be using DeviantArt.
However, this does not accurately reflect each characters' popularity with kids, so there's really no way of knowing unless there's an official poll or something from TVTokyo.
