Note that none of these address neural regeneration (after concussions, as claimed by oneshtein) because I'll leave that for the supporters to demonstrate.
I won't talk about Lion's Mane specifically, but there is a ton of science about things that induce neurotrophic growth factor, which some claim Lion's Mane to do, and research in concussions, depression, and Alzheimer's disease/dementia. These drugs are for the most part pretty new and quite expensive. Interestingly a lot of them are NMDA agonists, which... a drug you have heard of that works on that receptor is Ketamine, which has become popular for depression - leading a divergence of theories for why it works for depression - the most common being there is some therapeutic value in the dissociative state/"hallucinations", while a minority have claimed that it's actually the NMDA agonist property that is triggering neurotropic growth factor to repair brain damage, and the disassociation is a side effect.
You say all of these things and claim "there is a ton of science", but I ask for scholarly links to learn more. I don't trust anyone's word at face value on empirical topics, and I also don't know where to begin looking. "There are studies related to this out on PubMed." Show me! Phrases like this annoy me greatly.
Yeah, psychology studies are weak like that. Here is one with links to many other in vivo and in vitro studies, including some dealing with NGF and stroke (mice and rats). Quality varies.