Any notions of operations in basic postulates of lambda calculus
You can think of application $MN$ as an algebraic operation, where the operator has been elided for convenience. Instead of $MN$ some people write $M @ N$, or even
$$
apply(M, N)
$$
So $apply(\cdot, \cdot)$  is a binary operation, and, as @chi points out,
 $apply(\cdot, \cdot)$ is is neither associative nor commutative. The precise nature of what $apply(\cdot, \cdot)$  does depends on exactly what $\lambda$-calculus you have in mind.