How would you recommend booking the value of a lawsuit (asset & liability) on a financial statement?

GAAP says that for all contingent liabilities (and that includes law suits)…

If you are likely to win the law suit, you do not record anything nor do you even need to report it.

If you are likely to lose and can measure the loss, you should accrue it. If you can't measure the loss, then you make a note in the financial statements.

If you can not determine whether you will win or lose, you will make a note in the financial statements (regardless if you can measure it).