Probably liuhta (dialectal) + -e with fronting to *liyhde (*liühteh, compare Ingrian lyhe, Karelian lyyheh, liyheh, Ludian liuhtes). The form lyyhde found in Eastern Finnish is the original; the originally Western form lyhde likely derives from this with the -yy- shortened to -y-. This is likely by analogy with a sound change in Eastern Finnish that made certain short vowels long before a syllable-final -h- (e.g. Western huhtoa, pyhkiä, rohtimet ~ Eastern huuhtoa, pyyhkiä, ruohtimet). If correct, lyhde with short -y- is basically a hypercorrection.