Lucy suffers from unrequited love for Schroeder. Lucy tries to get Schroeder's attention, but usually fails. According to the biographical book Schulz and Peanuts by David Michaelis, Schroeder's contentious relationship with Lucy was based on Charles M. Schulz's real life relationship with his first wife.
Lucy's opinion of Schroeder
Lucy's love for Schroeder began on January 27, 1953. Ever since then, she has been madly in love with him. She is constantly seen leaning on Schroeder's piano, trying to get his attention, but usually failing. Schroeder would rather play his piano than listen to her. Lucy has tried almost everything, from just talking to him to walking over and kissing him.
Lucy's love for Schroeder has made her do crazy things. She even mentioned that the only reason she joined Charlie Brown's baseball team was because she loved Schroeder, who is the catcher, and frequently tells Charlie Brown to tell Scroeder that she thinks he is cute.
Lucy uses two main tactics to get Schroeder's attention, both involving Beethoven. Many times she acts like she is also a huge Beethoven fan, thinking that will impress him. She says he was a great composer and a great musician. She tries to give Schroeder pictures and statues of Beethoven, but he never accepts them. She even pretends that she celebrates Beethoven's birthday on December 16, like Schroeder does.
The other way Lucy tries to get Schroeder to notice her is by trying to convince him that Beethoven was not that great and making rude coments about him. However, anytime Lucy tries that, Schroeder normally pushes his piano foward, making Lucy fall off of it, sometimes getting hurt.Lucy has tried other ways to get the boy's attention too. She often tries to kiss him, sometimes succeeding, but often ending up accidentally kissing Snoopy.
Lucy constantly sees herself as being in competition with the piano, which she has even stolen and destroyed, by throwing it into the Kite-Eating Tree or into the sewers, but earning her none of Schroeder's love or affection.
Lucy sometimes does not seem to like the fact that she is in love with Schroeder. Sometimes she is upset that she chose to fall in love with a musician who will never love her back. In one storyline, she tries giving up on loving Schroeder, but after a week, she discovers she is unable to do it.
Lucy has mentioned marriage with Schroeder many times, even offering to fry his coffee every morning, but Schroeder is not interested in marrying her (or getting married at all). When Lucy annoys Schroeder so much he leaves the room, Lucy says, "my aunt Marion was right. Never discuss marriage with a musician."
Schroeder's opinion of Lucy
Schroeder is either very aloof, or does not appreciate, Lucy's love for him. Schroeder does not like how Lucy always leans against his piano, and many times, he throws her off of it. He says, it is impossible for him to like Lucy, because Beethoven was a lifelong bachelor, and Schroeder feels he must emulate every aspect of his idol's life, even if it is insinuated that he reciprocates Lucy's feelings. Schroeder does not seem to be particularly interested in any girls, but it seems that he prefers Lucy to others. For instance, in one strip, where Frieda, who also seems a little interested in Schroeder, and Lucy are both leaning against Schroeder's piano, Lucy becomes physical with Frieda and Schroeder takes Lucy's side.
A few strips have shown that Schroeder has some feelings for Lucy. For instance, in the strip from May 16, 1966, part of a storyline in which Lucy and the rest of her family move away that was later adapted as the TV special Is This Goodbye, Charlie Brown?, Schroeder remembers the time he spent with her and is upset that he never got to say goodbye to her. He becomes frustrated with his music and mutters disbelievingly that he misses her, realizing that, despite his animosity towards her, Lucy has unwittingly become his muse and he cannot play without her. In an early strip, Schroeder tells Charlie Brown that he thinks Lucy has pretty eyes, though sometimes they are out of focus.
Some strips have suggested that Schroeder is open to the possibility of eventually marrying Lucy. For instance, in one strip when Lucy says, "Lets say we've been married for six months, and I make some beautiful tuna casserole. Then you come back from work and walk into the kitchen and say, 'What? Tuna casserole again?'" Schroeder replies, "I would never said that!" Schroeder then says to Charlie Brown, "Sorry I'm late, I got involved in a marital dispute."
In the strip from December 16, 1984, Schroeder kisses Lucy on the cheek but when Lucy turns around she sees Snoopy. Believing Snoopy was the one who kissed her, she runs away screaming, while Schroeder calls for her to come back. In the strip from January 27, 1985, Schroeder is seen dancing with Lucy.