No, you do not pay taxes on long-term disability payments.
If your third party sick pay W2 has an empty Box 1, no taxes taken out, and has Box 12 Code J (third party sick pay), then it is not necessary for you to submit this W2 with your return.
This third party sick pay (Code J) is not taxable. Your employer was required to generate the W2, but it is not necessary for you to file it. And, if you try to submit a W2 with a $0.00 in Box 1, the IRS will reject your e-file. You can return to the Wages and Income section and remove this W2 from your return if it is still present, or simply not add it.
If your third party sick pay is taxable (doesn't meet the above criteria), then simply enter it as an additional W2. If no taxes were taken out, then you may owe additional taxes on the income now, but that will be factored into your return when you add the W2.
