There isn't one serious cut on [L.A. Woman]….
[Morrison is] taking no chances about being taken seriously or with universal import. In fact he's not even writing his own snake lyrics anymore. Instead there's John Lee Hooker's "Crawling King Snake," a whopper of a readymade and proof positive that he and his boys are still listening to the roots….
[The] Doors have never been more together, more like the Beach Boys, more like Love (the band they originally played second fiddle to at the Whiskey or the Troubador or wherever it was)…. Morrison [sets] the tone with lines like "Why did you throw the jack of hearts away?" on "Hyacinth House."… In terms of what they're after here the Doors as a band never falter and there isn't one bummer cut on the entire album—obviously a first for them.
It's also the first time since "The End" and "When the Music's Over" that they've been able to pull off anything interesting in the way of long cuts. And there are two of them here, "L.A. Woman" … and "Riders on the Storm" …, both of them minor monsters. And I'll be a monkey's uncle if "The WASP (Texas Radio & The Big Beat)" doesn't showcase Morrison's finest command of spoken jive to date, far superior to "Horse Latitudes" and a demonstration of lyric supporting timing at least the equal of George Burns in his prime.
You can kick me in the ass for saying this (I don't mind): this is the Doors' greatest album and (including their first) the best album so far this year. A landmark worthy of dancing in the streets.
R. Meltzer, "Records: 'L.A. Woman'," in Rolling Stone (by Straight Arrow Publishers, Inc. © 1971; all rights reserved; reprinted by permission), Issue 83, May 27, 1971, p. 48.