Lamarckian and Genetic algorithm
In fact, you're talking about Memetic Algorithms. In the case of a neural network, supposing you have training samples, the individual learning may be done through an iteration of backpropagation. If you don't have training examples, you may apply some noise to the weights and keep the modification only if it performs better (hill climbing). Actually, any local search algorithm could be used.
Regarding the frequency of individual adaptation, this is currently a research topic, but you can find works that suggest applying the adaptation to all individuals at every generation as well as other works suggesting to increase this frequency gradually, since the last generations are the ones which need more fine tuning. Genetic algorithms are very good to find some good global solution, while local search is very good to find the optimal local solution. So the trick is to find the optimal solution region with GA and fine tune with local search.