Would a W2-G be filed under additional income for lottery earnings?

Gambling losses can only be deducted up to the amount of the gambling winnings.
Gambling winnings are reported on Form 1040 Schedule 1 on Line 8b. The amount from Part I of Schedule 1 Line 10 flows to Form 1040 Line 8.
Gambling Losses are reported on Form 1040 Schedule A as a Other Itemized Deductions. Gambling losses are not a one-for-one reduction in winnings. Your total itemized deductions reported on Form 1040 Schedule A must be greater than the standard deduction for your filing status to have any tax benefit.

To enter, edit or delete Gambling Winnings and Losses -

Click on Federal Taxes (Personal using Home and Business)
Click on Wages and Income (Personal Income using Home and Business)
Click on I'll choose what I work on (if shown)
Scroll down to Less Common Income
On Prizes, Awards, and Gambling Winnings, click the start or update button

Or enter w2g in the Search box in the upper right of the program screen. Click on Jump to w2g