The book of Luke is essential to the New Testament for several reasons beyond the fact that we get to "experience" Jesus and his short time on earth through another lens. Luke reveals his purpose in the first four verses of chapter one:
Many people have already applied themselves to the task of compiling an account of the events that have been fulfilled among us. They used what the original eyewitnesses and servants of the word handed down to us. Now, after having investigated everything carefully from the beginning, I have also decided to write a carefully ordered account for you, most honorable Theophilus. I want you to have confidence in the soundness of the instruction you have received.
First, Luke is the only Gentile (non-Jew) author to write in the New Testament. He is also a doctor (see Colossians 4:14), which means his account will include more medical and health details and language. He is also a learned Greek, which gives a sense of order and structure to his writing which is not as evident in the other three Gospels. His comments (above) suggest that he has been a meticulous reporter, "investigating...carefully" in order to produce a reasoned, thorough account of Jesus's time on earth.
Luke is also the Gospel writer who gives the most time and attention to the women who played a part in Jesus's life. In Luke's Gospel we hear more about Elizabeth and Mary; we hear more about miracles performed on women; we hear more about women setting good examples; and we hear more about the women who surrounded Jesus in some way at the end of his life.
Two of the most popular parables Jesus ever told are the story of the prodigal son and the story of the good Samaritan, and they are only found in this book of the Bible. This is not surprising, as Luke generally emphasizes Jesus's humanity and compassion in his account, and these are two good examples of those principles.
Finally, Luke is generally considered to be the author of both this book and the Book of Acts--kind of like part one and part two of a documentary. Keeping one means keeping both. The book of Luke is essential to the New Testament.
The gospel of Luke is one of the synoptic gospels, and it provides another testament to the divinity of Jesus as the Christ and his works as they were recorded in the gospels of Matthew and Mark. Like the two gospels in the New Testament that come before it, the gospel of Luke begins with the story of John the Baptist from his birth, and we learn further of Jesus' relationship to John as a cousin.
The early parts of this gospel pays particular attention to women: Mary, Elizabeth, Peter's mother-in-law. It is also in Luke that we find "The Lords Prayer," where Jesus taught his disciples how to pray with a beautiful text that is still utilized often in services today. Luke also include many details about the crucifixion of Christ as well as his resurrection.
Luke was also a gentile. The inclusion of gentiles into God's people is a theme that Paul will extensively discuss in his writings as Abraham was at one time a gentile, but was incorporated into and became the father of the House of Isreal. Consequently, Luke as an author, as well as his writings, builds a foundation for later texts from Paul making it a valuable addition to the New Testament.