Is it acceptable to use lambda calculus notation elsewhere?

Question

For example, using Leibniz notation, we can write:

$$\frac{d}{dx}e^x = e^x$$

But this isn't so easy using Lagrange notation.
Is it then acceptable to write this?

$$\left( \lambda x. e^x\right)' = \left( \lambda x. e^x \right)$$