John,
I've been using Castrol GT LMA for years in my Giulias and Milano with zero problems. It's rated DOT 4, which is better than DOT 3, so no reason not to use it. By the way, if you're in Newburgh, you missed Scott Klion's Hudson Valley tour two weeks ago (he's been leading a tour for three years now). We brought our '62 Giulia Sprint, so you're Spider would have had good company. Watch the events thread here, and think about joining the tour next fall.
Jim