Well, LOTR books existed before the teletubbies. So I think it’s the other way around.

Someone accidentally mistook a full strip of LSD as one dose just after he finished reading the books, and saw this weird twisted form of what was fresh in his memory, with weird shapes and bright colors, and got the idea to recreate what he saw on film. Others mistook it as a toddler program.

I think my hypothesis is much more likely.