The characters on How I Met Your Mother all have different dynamics with one another. Some are best friends, some are dating, some hardly seem to interact at all. Regardless, the nine seasons fan spent with them made for some very interesting character dynamics.
One of the strongest was the connection between Barney (Neil Patrick Harris) and Lily (Alyson Hannigan). They have quite a charming back and forth with one another, but there are some elements of their relationship that would make for an odder friendship in today's day and age. After all, there is a ton about HIMYM that did not age well. Barney and Lily would hardly be precluded from that.
Seen As Family
One aspect of Barney and Lily's friendship that did not age well is the weird boundaries they have with one another. Their platonic connection is often said to be "like siblings" with one another. However, there are also many moments when Barney seems to see Lily as a parental authority figure in his life. That sort of arrested development could hardly hoped to have aged well.
Relationship Meddling
It's a heartwarming moment when it's revealed that Barney saved Lily and Marshall's relationship. But what if she didn't want to go back to Marshall? It might have seemed like Barney was practically forcing her. This sort of meddling shows that Barney only respected Marshall's feelings about their break-up and not Lily's. Granted, Lily would manage to get Barney back by meddling in a number of his relationships.
Sexual Interest
Obviously, Barney harbors a great deal of sexual interest in Lily, but he is not the only one. When she finally succeeds at setting Barney and Robin up to date, she becomes oddly curious about what exactly their dynamics are like in bed. It might just be out of curiosity to know what two of her closest friends like sexually. However, it's still an invasion of privacy that makes their friendship take on an extra level of strange.
Living Together
For a bit in season two, Barney and Lily actually live together. Both make some decisions during this time that did not age well, however.
Barney, for one, uses Lily to try to slip away from women he's not interested in. Lily, on the other hand, takes complete control of the apartment and practically makes it her own. Both of them engage in actions (like cuddling, for one) that could be construed as strongly relationship-oriented and it pushes their platonic friendship out of the way.
The Share Bear
In the season four episode, "Benefits," Barney is struggling with his romantic feelings for Robin and he decides to crash Lily's class to take the Share Bear away from her and vent his own feelings.
This is a weird trope in hangout comedies. Whenever one of the characters is a teacher, their friends always feel like they can just waltz right into their classroom. What kind of school lets someone like Barney Stinson into a kindergarten class?
Blackmail
This is not the only time that Barney interferes with Lily's career. He also uses elements of it when he blackmails her into keeping her silence about any number of secrets over the course of the show.
To be fair, Barney blackmails every character, but that doesn't really make it any better. Their friendship ages poorly a little more every day because a real friend would never blackmail another.
Secrets
Speaking of secrets, it's not like Barney's actions are the only ones that aged poorly. Lily was to blame for a number of moments that would make fans cringe in 2020 (like when Barney dated Nora, pictured above). For example, Lily is absolutely atrocious at keeping the secrets that Barney goes to such great lengths to protect.
It's one thing to have a hard time keeping your mouth shut. But Lily knows how bad she is at keeping secrets and she still seems to go out of her way to blab about them.
Barney's Techniques
A lot of Barney's character has not aged well, especially his manipulative and slimy tactics for sleeping with random women. Lily is rightly upset by a number of these techniques that Barney uses, but she still seems to abide by him.
The most she ever chastises him is when she calls him a "son of a b----." It shows that she's a loyal friend, but the fact that Lily hardly seemed to care that much is a bit of a question mark in today's world.
Mermaid Theory
On occasion, Barney would say something incredibly insulting to Lily, often without even realizing how offensive it was. When he spoke about the "mermaid theory," though, he knew exactly what the insult was. When Lily is pregnant, he evokes the "mermaid theory" to imply that Lily is no longer attractive and that Marshall will eventually grow accustomed to this, as he sees it, "fact." It hardly aged well at all.
Attraction
One of the biggest aspects of Barney and Lily's relationship that would not age well is the clear attraction that Barney has to Lily. It goes a lot further than just finding her pretty, though. Barney actively makes attempts to see Lily naked, especially in "Ducky Tie." He goes so far as to learn how to cook in a Hibachi style and master the craft just to be able to achieve this strange goal. It's a very manipulative thing for a friend to do.