Barney and Lily have a unique friendship, which is for the most part platonic. The two of them met sometime in 2001, after Barney had met Ted and Marshall. They mostrar más of a stereotypical brother-sister relationship with them making fun of each other and coming to the other for advice. Despite this, they have shown to have a small interest in each other sexually.
From Barney's perspective, he most likely sees Lily as his best confidant despite knowing that she can't keep secrets. Barney let her know that his childhood dream was to be a professional violinist. Also, Lily was the first person...

*Season 1
Barney introduces Ted to Robin with his "Have tu met Ted?" line, which eventually led to her joining the gang and becoming Lily's best friend. Later, Lily would run into Barney's ex-girlfriend, Shannon, who gave her a video tape to return to Barney. Being curious about what's on the tape, she gives Barney a decoy and then she and the rest of the gang plus Victoria decide to watch it after seeing Barney destroy it. They play the tape and see a younger, long haired Barney crying and begging for Shannon to take him back, this upsets Barney so he runs away from the gang. When they find...