I have a very old 66" lemonwood longbow and I'm trying to determine string length.  It's been in the family for years and has an old 60" string for it.  That seems pretty short for a 66" longbow?  The bow is in perfect shape and I'd like to buy a new string and do some shooting with it.  Any advice on how long of a string I should purchase and what kind of brace height I should shoot for?

I would shoot for a 63" string and a 6" braceheight.  Is it an old Pearson?  Those are nice.

Generally for a longbow, having a string about 3" shorter is what you want.
 If you plan to shoot this old bow you really need to reeducate it to bend and recover. This should be done slowly and in incremental steps. It would be a shame to make splinters of it and if done correctly it will shoot again as it did when it was first built. Lemonwood is quite brittle and will fret badly if forced into submission.

Also, be mindful of its MC, my old lemonwood (1940s) exploded after it dried out, she was a sweet shooter when she lived.