I am in a solid position to win a major lawsuit. I would like to show this deferred asset on the financial statements, however, I'm stumped as to where to put it on the debit side. The purpose is to strengthen the position of the company on the financial statement.

Debit some sort of Receivable account. Perhaps Lawsuit Receivable

If you were going to lose, you would:
Dr. Loss
Cr. AP

So now that you will win you will:
Dr. AR
Cr. Gain