A Japanese study from March 2019 study says yes.
It found that oral intake of Hericium erinaceus (Lion's Mane) fruiting body "significantly improved cognitive function and prevented deterioration".
The study was randomized, double-blind, placebo-controlled, and lasted for 12 weeks. It subjected participants to three different tests to measure cognition.
Note that Lion's Mane fruiting body was used as the supplement in the study, NOT mycelium.
The study states, "Oral intake of H. erinaceus is a safe and convenient method for dementia prevention", citing hericenones and the way they affect the brain's neural networks in positive ways, such as increasing the neuropeptide Nerve Growth Factor (NGF). Hericenones increase NGF safely and naturally, and other studies point to it being an effective adjunct for Parkinson's disease, among other uses.
Multiple hericenones have been identified including hericenone A, B and I. Lion's Mane Fruiting body is also rich in beta-glucans.
While cardiovascular disease is known as the most lethal disease in the West, cognitive problems are very pervasive issue in aging countries like the U.S. Neurodegenerative diseases like Parkinson's disease are extremely debilitating, but the loss of cognitive function in dementia is equally devastating for those affected.
More studies will continue to explore whether Lion's Mane may be able to assist in the prevention and the treatment of cognitive disease. So far it looks promising.
Yuusuke SAITSU, Akemi NISHIDE, Kenji KIKUSHIMA, Kuniyoshi SHIMIZU, Koichiro OHNUKI. 2019. Improvement of cognitive functions by oral intake of Hericium erinaceus. Biomedical Research Volume 40, Issue 4, Pages 125-131. https://doi.org/10.2220/biomedres.40.125