Has lamarckism been discredited?
The question is interesting at many levels. Of course, in biology and in any other science there is no absolute or 'objective' truth about some given phenomenon if we really care to look at the nuances. Lamarck seems to be vindicated mainly by a wave of empirical work on patterns of transgenerational inheritance, particularly in the field that is known as epigenetics. You can read a good intro-level review here for some recent developments, some particular examples here, or a more conceptual reading here. 

As an evolutionary biologist myself, I will say that most other biologists acknowledge that epigenetics and transgenerational inheritance are important and have solid empirical support, but (for various reasons) some of them are hesitant of calling that 'Lamarckian'. 

By the way, Dawkins was a very effective science popularizer, but he does not practice science nowadays, and many of his ideas lie in what is known as 'scientism', which is a blind confidence in science as an absolute truth that is inflexible. The same applies to many positions of Steven Pinker, deGrasse Tyson, etc.