Well, I believe you're actually referring to the one in the beginning of Empire Strikes Back after Luke was saved by Han Solo. To say the truth, that was because Luke and Leia never knew they were “siblings,” let alone twins. They wouldn't even know until midway through Return of the Jedi.
It's well known that Star Wars lead characters Luke Skywalker and Princess (now General) Leia are brother and sister. The estranged siblings didn't know about their familial relationship until "Return of the Jedi." They even shared a passionate kiss in the previous movie, "The Empire Strikes Back."
Following the Wampa attack during the movie's opening scenes on Hoth; Leia, Han, and Chewie visit Luke in the infirmary. Leia is annoyed with Han, who insists she has feelings for him, so she kisses Luke to prove she doesn't. Presumably, the scene was simply meant to make Han jealous.
No, she didn't consciously know this - i.e. she wasn't aware of it. Leia meant that the connection she always felt towards Luke now made sense - the one that she originally misinterpreted as sexual love, but realised was (appropriately enough), sisterly love.
Yoda spilled the beans about Luke having a lost relative before he died. Obi-Wan's ghost would later confirm it as Luke's twin sister. Luke himself quickly realize it's Leia after the subtle clues Obi-Wan mentions to him.
Darth Vader didn't learn he had a daughter until Return of the Jedi, when he stood before Emperor Palpatine. The Emperor's power probed Luke's mind, attempting to goad him to fall to the dark side, and he discovered Leia's existence. "Sister," the Emperor taunted.
After Leia and Luke's lips lock in Lannister love, our wookie friend vocalizes what seems to be his approval. However in hindsight, Chewie was more than likely saying “Your species' obsession with sibling mating is a curious one, I've seen your browser histories”.
While Return of the Jedi would ultimately reveal them to be siblings, A New Hope implied Luke's attraction to Leia throughout, while the two kissed multiple times in The Empire Strikes Back, with further romantic moments ending up on the cutting room floor, as seen in the movie's deleted scenes.
In a medical center shortly after, Princess Leia checks on a recovering Luke, and in an effort to make Han jealous, she kisses the bedridden hero and walks away. At the time, neither Luke nor Leia knew they were siblings,...
Alderaan's princess knew she had been adopted by Bail and Breha Organa after the Clone Wars, but she had no idea who her parents were. That was until Luke Skywalker told her the truth - that he was the son of Darth Vader, and that she was his sister.
There is a deleted scene from The Empire Strikes Back that makes the kiss between twins Leia and Luke even more uncomfortable due to their now-known relationship as biological brother and sister. In an alternate version of the scene featured in the movie, Leia is remarkably more affectionate toward her brother.
Luke and Leia only discovered they were twins in Return of the Jedi despite being Force-sensitive.
In hindsight, Luke had the luxury of carrying his father's real last name because he was a nobody hidden in the Outer Rim Territories. Leia, on the other, was adopted into a well-known and prominent family, hence why she was given the name Organa.
Leia's journey yields a time dilation of 62.6 days; however Luke experiences a time dilation of 700.8 days (1.92 years). The students concluded that Luke is therefore 1.75 years younger than Leia, possibly rendering them the first twins ever to have over a year between their ages.
“While it is not demonstrated in the film, the twins will actually have aged very differently due to their extensive travelling at speeds close to that of light. “Despite Luke's journey being twenty five times longer than Leia's, the time dilation he experienced was only around ten times larger.
did luke and leia ever figure out who their mother was? i only remember them talking about anakin :( Yes, they did. Eventually, Leia contact her good friend Pooja Naberrie to discuss her mother so they definitely knew about Padmé Amidala and the fact she was their biological mother.
As Leia tells the story, it becomes clear that it is Han's undying devotion to the causes he champions that Leia fell in love with. She explains that his willingness to risk his life saving a place that he hates made his light shine through even the gruffest exterior.
During the Battle of Yavin, however, when Vader almost succeeds in killing Luke - Han saved him - after this Leia's opinion of Han changed - and they slowly fell in love with each other. Han and Leia developed a relationship that would last throughout the war.
Leia kisses her twin to prove she's not into Han.
“Fakeout” Luke finally speaks with his sister after many years of self-imposed exile. They have a touching conversation at the end and Luke gives Leia a brief kiss on her forehead. So the final tally is Princess Leia gives her brother Luke Skywalker five kisses and Han Solo got eight.
Leia wasn't really in love with Luke. She just did that to shut up Han Solo who was flirting with her on the falcon. Nothing ever came of it and it was never discussed ever in the saga's future episodes.
Not only was Leia incredibly strong-willed, but she also had the blood of the Chosen One coursing through her veins. This knowledge, paired with some more recent lore tidbits, suggests she was one of the most powerful Force-users to exist, perhaps even surpassing Luke.
While a mistake in real life, the canon reason that Leia embraces Rey before Chewbacca is due to Leia seeing Rey as a lost soul and surrogate daughter, establishing a strong relationship that will grow through the sequel trilogy.
Even as a newborn, her instinctual connection to the Force could have helped her form a bond with Padmé. It's also possible that Leia gleaned images and impressions of her mother through the Force even after Padmé's death.
In A New Hope, Obi-Wan and Leia never spoke face-to-face, only communicating through Leia's recorded message to the former Jedi Master.