I've heard this rumor for years, both from pro- and anti-drug people, and it is not true. According to this review of LSD's pharmacology, its half-life in the body is about 5 hours, with it being completely cleared within about 15-28 hours. There is no evidence that it accumulates long-term in fat, cerebrospinal fluid (CSF), or anywhere else in any pharmacologically significant quantity.
Reference:
"The Pharmacology of Lysergic Acid Diethylamide: A Review" _CNS Neurosci Ther._ 2008 Winter; 14(4): 295–314. PMID: 19040555 DOI: 10.1111/j.1755-5949.2008.00059.x