Why is lambda calculus a "calculus"?
A calculus is just a system of reasoning. One particular calculus (well, actually two closely related calculi: the differential calculus and the integral calculus) has become so widespread that it is just known as "calculus", as if it were the only one. But, as you have observed, there are other calculi, such as the lambda calculus, mu calculus, pi calculus, propositional calculus, predicate calculus, sequent calculus and Professor Calculus.