Spiralize squashes: Cut necks off squashes and cut each in half crosswise. (Reserve bulbous ends of squash for another use.) Using a thin spaghetti blade in a spiral maker, spiralize squash chunks. (TIP: If noodles are very long, trim with kitchen shears to desired length.)
In a large skillet on medium, melt 4 tbsp butter. Add noodles and salt and cook, tossing occasionally, until tender, 7 to 10 minutes. (NOTE: To prevent browning, reduce heat and add water 1 tbsp at a time, if needed.) Remove skillet from heat; stir in remaining 2 tbsp butter, Parmesan, Grana Padano, pepper and lemon zest. Season with additional salt, if desired.