Why did Warren need to invent communication lacrimas?
A reason could be that the usual Lacrima crystal, which is shaped like a crystal ball, looks a bit bulky. 

Why did they need to "invent" what were basically cell phones when they already had lacrimas to communicate over long distances? The Miniature Communication Lacrima invented by Warren which, as you pointed out, is shaped like cell phones are much smaller in size but has the same functionality. This makes it easier to carry around.