Dating an Eames lounge chair through patent label  

If the greatest patent number date is 1964, it cannot have been made prior to that, and it seems reasonable to assume that it probably wasn't made all that much after either...  I don't know how often stickers were updated though.  I guess looking at a list of all the Herman Miller patents would be the way to check.  Realistically, I would think 64-66 would be your year given what you have noted, but the metal Herman Miller tag pictured is from the 70s (or at least I thought it was(?)).
Wouldn't a 60s chair have a round tag?  Anybody know more precisely what years the tag pictured was used?
I'm not having any luck with this thing either...   http://www.hermanmiller.com/about-us/who-is-herman-miller/policies-and-l...     "no results found"???

Yes, manufactured after 1964. No, not necessarily soon after 1964.
The "herman miller" label doesn't tell us much; that style was used from 1970 or earlier until the late 90s.  And the list of patent numbers on the other label didn't change much, if at all, after the last one shown above (3,124,390) was added to it.  Here, for example, is a chair made in 1978:

Been away for way too long. The update has made it hard to keep up. First, I don't know anything about those patent numbers. However, the black rectangular Herman Miller labels appear to be used from the 70's through the early 90's. I've onwed one with the C. Walter label as well. If I remember correctly, the date was stamped on the inside of the plywood. Mine was from the 80's, so unless Mr./Ms. Walter worked across a couple of decades, my wild guess is yours is also from 80's. I suggest you remove the cushions and see if you can find any date stamps. Good luck and keep us posted.