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Look in the driver's door jamb. Under "AXLE" it should say "C1" or "31". C1 = 3.73 LS, 31 = 3.73 Non-LS. If the sticker is gone, look at the diff for a tag. Somewhere on there it says 3 73 or 3L73. If the L is there you have a LS diff...
I used Royal Purple with it already in there. But I believe it's 4 oz. But start with 2 oz. and see if there's chatter. If it chatters, add 2 more oz.
EDIT: Oh, and you might look at the '08 diff cover. It's pretty nice, and not too pricey:
Let's see if this link works... I got mine from Ed "FTE Parts Guy", but since then he got laid off. I understand he's at Y2K Parts. I paid ~$55 shipped to my door, but you need longer bolts (1 1/4") since the cover is thicker than the standard steel one. Here's the link (you want the 6.4L one, obviously): Y2KFORDPARTS