Lamarck was one of the first scientists to propose the idea that organisms changed over time. A major proposal he had was the idea of inheritance of acquired traits. This idea states that a new trait or ability obtained in one's lifetime could be inherited by their offspring for future use. When Darwin began further expanding on evolution, however, this idea was found not to be correct.
The idea that Lamarck influenced the most, is that in order for traits to evolve and change, they must be heritable. However, Lamarck believed in evolution involving the use and disuse of organs: an organ that is more utilized will be enhanced upon, but an organ underutilized will degenerate. Although Darwin believed in this sort of change in organisms, he adopted a different approach. Rather than new traits or changes taking place within lifetimes as Lamarck had predicted, Darwin hypothesized that these sorts of drastic changes could only take place through a continuity of variation over longer periods of time.
Darwin may have been able to develop his theory without Lamarck's ideas serving as a precursor. However, Darwin would potentially have to consider many other possible hypotheses, for Lamarck's work wouldn't have been readily available to critique or expand upon.
Darwin did not wish to rush publishing his work on evolution/natural selection, as he had a lot of thorough research to continue pursuing. Also, had he published it earlier than he did, he could have potentially received far more religious opposition for a theory that had been unpopular, and perceived as blasphemy.
Source(s): http://www.majordifferences.com/2013/05/difference-between-darwinism-and.html#.V7_c99QrKt8