Sir Charles Lyell, was a Scottish geologist who grew up in the Grampian Mountains as a child. His father was a naturalist who had a huge stock of books that contained many subjects he studied, including geology. During Charles childhood, his fascination with the study of earth was quite prominent by the way he disliked school and decided to skip it and go to the New Forest. Charles was viewed as a strange boy by many people in the village he lived in, but that would prove to be a misjudgment once Charles furthers his studies in his adulthood. Since Charles was never deterred to stop his studies, he pursued his passion with the help of
others such as Naturalists Alexander von Humboldt and Georges Cuvier. Around this time, "Charles was
rapidly developing new principles of reasoning in geology and began to plan a book which would stress that there are natural (as opposed to supernatural) explanations for all geologic phenomena," (https://www.britannica.com/biography/Sir-Charles-Lyell-Baronet) so he decided to travel to countries such as Italy and France to prove his theories. Once he traveled to Mt. Etna, he finally discovered that his theories were correct. From the results of his trip, Charles returns from his trip and began to write his book, Principles of Geology, that discussed many principles, facts, studies and inquiries of his studies. This novel caught the attention and admiration of Charles Darwin himself and led to him using it for reference for his own studies when he traveled around the world.
I believe that Sir Charles Lyell had a great influence on Charles Darwin because of Darwin's main studies: evolution. Darwin had to travel to many different locations to perform his studies and some of the destinations he went to were uncharted and potentially dangerous for him. Through Sir Charles Lyell's book, Principles of Geology, Darwin was capable to learn about geology and it greatly helped him on his travels. He even equipped the book with him whenever he decided to set out on a journey along with other materials. Without Lyell's studies, it would be possible that Darwin could have had a lot of problems charting unknown islands.
If it wasn't for Lyell's geology proficiency and social circle, I think Charles Darwin might not have actually been willing to do too much traveling of his own since he lacked the skills of exploration. It would have made traveling difficult for him and it would have hindered his studies of evolution since many creatures live in very distant and treacherous locations. Since Darwin's main method of studying evolution was learning about an animal's origin of life such as their habitat, Lyell's book was of great use to him. However, as for Darwin's studies in evolution, Lyell didn't have much influence on that and even if Principles of Geology and the friendship both Charles would develop, Darwin would have been fascinated with the study of evolution since that interest sparked when he traveled on the HMS Beagle. The only possible influence that Lyell may have on Darwin in terms of the study of evolution, Lyell did introduce Darwin to Richard Owen, who was an anatomical.
Darwin's theories of evolution disturbed many in the church because it opposed their religious beliefs. The thought of evolving from primitive beings was unheard of during Darwin's time and it baffled many. And such beliefs of evolution still baffle people today. Darwin was bold enough to publish his work to the public since Christianity was a huge part of human culture and many people believed in it. So once Darwin released his book, their would be many people that would be enraged by his accusations. Although Darwin's work was unsurprisingly despised by many, it was a wise decision on his part to release his findings to the public because of the impact it made on society. With the findings of evolution shown to the public, the book is able to make an impact on others and open their eyes to new concepts to humanity's mysterious upbringing.
Sources: https://www.britannica.com/biography/Sir-Charles-Lyell-Baronet
http://www.macroevolution.net/charles-lyell.html
https://www.britannica.com/biography/Charles-Darwin/The-private-man-and-the-public-debate