Lily is a little more complex than the average TV Kindergarten teacher. While other sitcom kindergarten teachers can be aggressively quirky and scream 'kindergarten' in every way, from wardrobe to language, Lily is significantly more realistic. Yes, she loves her job, but she also loves her husband, her friends, her hobbies, and her wine (for better or for worse).
Lily doesn't always make the best decisions - although she may always have the best intentions, and while there are some aspects of her character that make her an incredible friend, there are others that might be offputting in real life. Whether or not these negatives can outweigh the positives is up to fans, though - would you want her to show up at your local bar?
Best: Always There To Help
Lily is, without a doubt, a great friend - and she's always there to help out. Whether it is putting together huge meals, helping friends with problems, or even rushing out on her own kindergarten class in the middle of an emergency, she'll do it. She's been there to help Barney convince the women that he brings home to leave in the morning, she's been there whenever Robin needed her, and she's shown that she's perceptive enough to do it without always having to be asked, too.
Worst: Patronizing
This may be a holdover from her classroom time, but Lily definitely becomes the mother to the group on a few occasions, and loves giving advice. Her advice may be solid, but it's clear that she thinks that she is the one in her friends group that has all the answers, and she is going to give them whether asked or not. At times, she treats the people around her like little kids, talking down to them and teaching 'lessons' the way she would in class (like stealing a baseball to get Ted's boss to behave nicely at the office). She even 'trains' Marshall like he's a dog, using sex instead of treats!
Best: Patient & Understanding
Lily might think that she knows best, but when it comes to her friends in trouble, she'll never judge. She is always understanding and knows when is the right time to bring something up. When Robin starts backing away during her pregnancy, Lily seeks out her old friend to find out why - and when she learns that Robin is afraid that Lily will abandon her, she understands, and reassures. And when she knows that Ted is struggling with Barney and Robin getting married, she shows him she understands, and it's ok - and that she struggles with unthinkable things sometimes, too.
Worst: Controlling
Lily attempting to train Marshall using sex as a reward isn't the only time that she tries to control everything in their lives. She likes to plan, and to force things to go her way - including those weird, awkward double dates and the photo montages that follow.
She wants to make sure that everything happens on her schedule, and the way she wants it to, and she is constantly telling her friends what to do.
Best: Creative
Lily might be a Kindergarten teacher by day, but she is an artist by night (or at least, occasionally in her spare time). Her art even eventually leads her into another job, where she is an art buyer for The Captain, and she makes a nice sideline selling her own paintings to vet offices - because they calm down dogs. Her creativity, and everything that goes along with it, is one of the best things about her.
Worst: No Boundaries
This is, admittedly, true of pretty much any character in a sitcom about a group of friends, because most of the stories and the jokes seem to require a group of people who have absolutely no boundaries. However, it's definitely true here. Lily gets ridiculously involved in her friends' lives - she breaks into Barney's apartment, and previously lived there and started changing the decor. She is especially bad with Ted, where she actively works to end his relationships if she doesn't think that his partners are good enough.
Best: Optimistic
Lily is hopeful and optimistic to a fault. She honestly sees the best in everyone - and even when it comes to Barney, someone who consistently behaves inappropriately, she sees the good (and ignores, for the most part, the bad). She never gives up on the idea of Ted finding love, and when she has separated from Marshall, she never gives up hope that they will get back together.
Worst: Cannot Keep Secrets (Except Her Own)
Lily has been shown to be absolutely incapable of keeping a secret - it's so bad that all her friends regularly reference it. And while this may seem cutesy on the show, being untrustworthy and incapable of respecting the secrets of other people is a pretty toxic trait.
This is especially true because it is shown that Lily is absolutely capable of keeping her own secrets - from her application to an art program in San Francisco to her credit card problems, she clearly can keep secrets, she just doesn't want to keep them for other people.
Best: Adventurous
Lily might not always make the best decisions, but she is often guided by a spirit of adventure, and that's a wonderful thing. Her art program in San Francisco didn't work out well, but she was brave to try it in the first place. She's willing to try new things, go on roadtrips, embrace change, and do it all with a smile. She even changes career multiple times, to try and make sure she is doing the best thing for her.
Worst: Holds A Grudge
Lily is the queen of grudge-holding, and there's even an entire episode about it. It's revealed that Lily, after someone 'wrongs her' (in her eyes, anyway) imagines them spontaneously combusting, and then they are 'dead to her'. She is willing to do this for things as minor as giving her caffeinated coffee instead of decaf, or major things, including the way her father behaved for... well, most of her life. It's actually impressive that she's never done this to any of the core group, given how often it seems to happen.