Darwin's theory of evolution stated that all species developed through the natural selection of small inherited variations that increase the individual's ability to adapt, survive and reproduce.
Lamarck's theory of evolution stated that the physical changes that occurred in the organism during its lifetime, for example, the development of an organ or a part of the body due to an increase in its use, could be inherited by its offspring.
The situation described in the question "the person who dyes their hair green" represents a change in the organism's characteristics during its lifetime, which is compatible with Lamarck's theories.