It is well known that environmental hazzards can increase mutation rates. I am not aware of any data that are relevant to the question whether behavioral stressors might also influence mutation rates, germ line - not somatic. This would obviously be a clever evolutionary trick: keep rates low when things are going well, and increase rates when things are not going so well. It may also be wishful thinking.
Related is the issue of different mutation rates for different sites. Does it make any sense, at all, to think that different stressors (i.e. their biochemical consequences) could differentially affect different sites as measured by variations in mutation rate? Again, probably not, but I am curious.
The old nature/nurture issue is rather uninteresting as originally phrased. However, there are possible questions that I see lurking: Not really Lamarkian issues per se, but variations on the theme that environmental adaptations might end up having genetic consequences. Think back, for example, to the Baldwin effect, where the organism's phenotypic plasticity can potentially hold the organism in a viable state until a mutation "happens to come along".