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Isn't performance a major concern in LSL. That might be an issue with putting a neural network into LSL.
Bone
You could create a neural network in LSL. The language is capable of creating one. However, lack of a 2d array, or really any arrays, would make it very cumbersome. All of the matrix math would have to be done using the lists that are built into LSL.
LSL in its current form is fairly slow. Once they switch the VM to mono, it will be considerably fast. This switch has been "just around the corner" for about 2-3 years now. However they are testing it now, and it should be ready sometime soon. Of course, this will not add arrays to their scripting language. The mono upgrade is only at the VM level, at least for now.
An interesting approach might be a hybrid solution. Linden scripting language does allow communication to outside servers. This is done mostly through HTTP. All, or part of, the neural network processing could be done outside of the Second Life world. At the very least the slow process of training the neural network could be done outside of Second Life, and execution of the network could still be done in LSL.
Jeff