Tippi Hedren, perhaps most famous for her role in Alfred Hitchcock's The Birds, is an actress of formidable gifts. Hitch himself said, when directing her in that classic film, that Hedren had "a faster tempo, city glibness, more humor [than another frequent Hitchcock heroine, Grace Kelly]. She displayed jaunty assuredness . . . and she memorized and read lines extraordinarily well."
Now 84, Hedren remains active in showbiz—for example, appearing in Cougartown (as herself) as recently as 2013.
But her role as an animal-rights activist and conservationist might well be Hedren's most lasting legacy. For decades, her Roar Foundation and the animal sanctuary, Shambala Preserve, in California have advocated for big (and not so big) cats—from lions and leopards to bobcats and servals—and she's been honored with a host of humanitarian and conservation awards through the decades.
In 1971, LIFE photographer Michael Rougier spent time with Hedren; her teenage daughter, Melanie Griffith (from Hedren's first marriage, to Peter Griffith), her then-husband, the agent and movie producer, Noel Marshall; and others at their home in California. Also in attendance: Neil, a 400-pound mature lion, who occasionally slept in the same bed as Griffith and, as these pictures attest, had the run of the house, from the kitchen to the living room to the swimming pool.
Hedren has since acknowledged that it was "stupid beyond belief" to put her family at risk by allowing an animal with "no conscience or remorse genes" to roam free. On that, at least, we can all agree—even if these pictures make Neil look like the world's biggest pussycat.
Liz Ronk, who edited this gallery, is the Photo Editor for LIFE.com. Follow her on Twitter at @LizabethRonk.