The 'puff' effect in puff pastry is produced by an alternation of fat/dough layers. When heated, the water in the dough will become steam and try to scape (hot air go up). Since steam and fat don't mix, this effectively creates pockets of trapped air in between the fat layers. The steam eventually manages his way out leaving behind a layered dry gluten skeleton.
With this picture in mind, the type of fat used plays two roles:
Workability. The fat needs to be soft enough to be spread over but hard enough to be trapped without 'sleeking' when layering. The traditional recipe asks for butter, but many commercial brands use hydrogenized vegetable oil as well, which are fairly stable. In principle, you could use lard or lamb fat.
Taste. Well, unless you are making a lamb pie, lamb fat might be a bit too strong.
As for the acid, I don't see how it could play a role in this process which is mostly mechanical. I also disagree with the claim that traditional French puff pastry takes a bit of lemon juice. Marie-Antoine Carême, the "chef of the king's and king of the chefs" don't mention lemon or vinegar in his treatise about puff pastry. More on the modern side, neither do Alain Ducasse, Pierre Hermé (who curates the Larousse des desserts) or Michel Roux. So maybe some recipes ask for it, but it is definitively not the rule.
Most of the industrial puff pastries do contain either lemon or vinegar, which they label as 'acidity regulator' in the ingredients list. I believe this acts as an anti-oxidant to increase shelf life and prevents rancidity. Another explanation (a long shot) might be taste. The traditional method for making butter in France involved fermenting the cream in a clay pot before buttering. One of the distinctive aspects fermentation brings is acidity.
