how did data's daughter lol get her name?

Answer 1

In the Star Trek fictional universe, Lal is the name of Lieutenant Commander Data's gynoid "daughter" whom he created. Lal's first and only live appearance was in the episode "The Offspring". The initial asexual version of Lal was portrayed (in heavy makeup) by actor Leonard Crofoot. After chosing its race and gender, the subsequent droid was portrayed by actress Hallie Todd. While referred to throughout as an android, the later version of Lal is technically a gynoid – a robot resembling a human female. Her vocal abilities are more advanced than Data's. She can use contractions such as "don't". She also can feel emotions, to some extent.
In the episode, Data, having recently attended a cybernetics conference where a new sub-micrometre matrix transfer technology was introduced, returns to construct an android and transfer his own positronic pathways to the new android's brain. Data names the android "Lal", which means "beloved" in the Hindi language, and introduces it to fellow Enterprise crewmembers as his "child".
Picard is dismayed by Data's decision to pursue such an undertaking in secrecy and is extremely concerned about the reaction when Starfleet learns of the existence of another Soong-type android. However, Data is determined, and goes immediately to work in raising Lal. Lal's personality and sentience develop steadily to everyone's delight. Although Lal encounters difficulties in mastering the nuances of human behavioral norms, she displays emotional and functional abilities that surpass Data's, including the use of verbal contractions. In response to Lal's "frustration" at her challenges, Data explains that although neither of them may become fully human, the struggle itself can bear worthwhile fruits.
The Offspring is notable in that it was the directorial debut of Jonathan Frakes. His character, William Riker, did not appear much in the episode, but his first appearance was quite memorable: Riker sees Lal at 10-Forward but does not realize that she is Data's daughter. Lal, trying to emulate human rituals, flirts with him and even kisses him. At that moment, Data comes in and asks Riker "What are your intentions towards my daughter?"
Admiral Haftel arrives from Starfleet Research, interviews Lal, and insists that she be relocated (without Data) to the Daystrom Annex on Galor IV. Upon learning of Admiral Haftel's plan, a frightened Lal visits Deanna Troi, who immediately senses the authenticity of Lal's newly found emotion. Lal, growing more unstable, flees Deanna's quarters, fearing what will happen when Haftel takes her away; Troi watches in dismay as Lal begins a difficult retreat to Data's laboratory. Troi summons Data to the lab, where Data (with Admiral Haftel's assistance) struggles unsuccessfully to save her from her rapid positronic cascade failure. In her last moments of life, Lal expresses sadness that Data is unable to save her, but thanks him for her life and tells him she loves him. Data isn't able to feel the emotion of love, so Lal tells him that she will feel it for them both. Lal suffers complete neural system failure—dies—a little more than two weeks after her activation. After Lal's system failure, Data transfers her memories to himself.
Several years later, when Data meets his mother—the former Juliana O'Donnell—she learns of Lal's existence when she comes across a portrait of Lal that Data has made. Data tells her that the matrix he created for Lal was not stable and collapsed. She informs Data that creating a stable positronic matrix was not very easy, and that she and Dr. Soong lost five androids before creating Lore.