Deductibility of Lawsuit

If you pay a legal settlement as part of doing business, the settlement is a deductible business expense, except that you can't deduct anything related to illegal conduct.  (Not all business disputes involve illegal conduct, of course.)

If you pay more than $600, you need to collect their tax number with a W-9 form, and issue a 1099-MISC (unless they check the box on the W-9 that they are an S- or C-corp, in which case you don't issue a 1099-MISC.).  If the payment is compensation for services performed by a subcontractor, you would issue a 1099-NEC.  If the plaintiff was an employee and the settlement is partly or all for lost wages, you would issue a W-2 as if it was regular wages and you are responsible for withholding the employer's share of social security and medicare like any other W-2.  

Once you issue the correct tax report (1099 or W-2), whether the money is actually taxable to them depends on their circumstances and is between them and the IRS.  

Yes, you can deduct the settlement fee as an expense on your return.

If you are making a payment of more than $600 you should send the party receiving the settlement a 1099 Misc.