Your sentence:
- Before I will lay out his argument, I will define my terminology.
Is correct as written, and means something different from your proposed alternate:
- Before I lay out his argument, I will define my terminology.
John Lawler wrote in a comment:
In a conditional phrase like the one before introduces, the modal auxiliary will is limited to its deontic sense of be willing instead of its epistemic (expected future) sense. That's what makes the first sentence hard to process. That's also the sense Washington used it in.
His final sentence regarding Washington is in reference to FumbleFingers’ comment:
The Writings of George Washington: If there does not come a sufficient Reinforcement, we must either quit our God, and retreat to you, or fight very unequal Numbers, which I will do, before I will give up one inch of what we have gained.
When you begin a sentence with
Before he will do X, ....
You are using will not as a neutral marker of the future but as a synonym for be willing. It’s like when your dad tells you to go clean your room and you answer No, I won’t! meaning that you refuse to do so, that you are unwilling to do so.
So that means:
Before he is willing to do X, ....
That’s like saying that:
He is unwilling to do X until....
Here’s another example of this deontic use of will with before:
- Before I will answer your question, you must tell me why you want to know.
In other words,
- I won’t answer your question until you tell me why you want to know.
Which is also:
- I am unwilling to answer your question until you tell me why you want to know.
All modal verbs in English have two modes of operation: the epistemic mode and the deontic mode. Knowing which is which is critical to figuring out which in this famous pair is the cry for help and which is the suicide note. :)
- I shall drown, no one will save me.
- I will drown, no one shall save me.
You should please see Professor Lawler’s linked answer for a bit more about this.