Well, I'll be! The writers didn't forget about Lana and her lack of a team change in nearly 100 episodes! I'll be honest: I'm a little surprised the writers decided to give Eevee to Lana, rather than to one of the other main characters, such as Ash or Lillie. While there hasn't been any concrete evidence that Lana is specifically a Water type Trainer, her great interest in and love for the ocean gave me the impression that she would prefer a Water type over any other type. It makes me wonder what the writers' plans are for Lana and/or Eevee.
Taking into account the events of the episode itself, however, I'm not at all surprised Lana caught Eevee. As soon as the episode began with Lana at home, I had a feeling that if anyone caught Eevee, it would be her. Eevee and Popplio's adventures throughout the episode solidified that impression. The carefree, fun-loving Eevee should be an interesting foil to the dutiful, slightly neurotic Popplio. It will be interesting to see how Eevee—or, rather, how Nagisa does under Lana's tutelage.
Was anyone else reminded of the starter trio episode? Popplio and Nagisa working together to escape first the Alolan Persian and then Team Skull reminded me of Litten escorting Popplio and Rowlet back to their Trainers.
On the contrary, Nagisa is guaranteed screen time, if for no other reason than to promote LGPE. One could argue that the fact that Lana caught Nagisa more or less guarantees Lana will get more screen time, since she is Nagisa's Trainer.
People who feared Ash catching Eevee might mean Eevee would usurp focus from Ash's other Pokémon, or that Ash would be less likely to end up with more evolved Pokémon on his team, should be relieved Ash didn't catch Eevee. Personally, I'm just glad someone actually caught Eevee, rather than it being a class pet or an unofficial/temporary capture.
All these assumptions simply based on the fact that Ash didn't catch Eevee in this episode? Just because Ash didn't catch Eevee doesn't mean he won't end up with a full team of six Pokémon (including Pikachu) by the time the League rolls around. Just because Ash didn't catch Eevee doesn't mean the League is going to be a joke, or that we're going to get "Cameron levels of stupidity." I get that people are upset Ash didn't catch Eevee, since he is long overdue for an addition to his team, but these assumptions are going a little overboard, aren't they? :/