The NREH is very different from Lamarckism. The latter is a theory of evolution based on the inheritance of acquired characteristics. If an animal builds up strength in its limbs, this limb-strength can be inherited by its offspring. There was no mechanism offered for how it happened, principally because there was no understanding of heredity. The NREH, on the other hand, says that organisms have a built-in capability of responding to environmental stress by making epigenetic changes. These changes often involve the turning on of cryptic genes that produce phenotypic changes that are usually adaptive to the new stress. The evidence for genetic changes stimulated by stress is manifold. That they are often adaptive is induced from the observation of rapid adaptive evolution as in finch populations that rapidly fill new niches. See my book for more examples.