If I received a lump sum payment from Social Security dated back to 2011 for both of my children, because my ex-husband is disabled. Do I need to pay taxes on that?

A portion of the lump sum Social Security back payments may be taxable.  If the payment was received in 2019 it will be reported on your SSA-1099 received in January of 2020.  The payment is entered on the 2019 tax return.

Go to this IRS website for information on the back payment and the worksheets available in Publication 915 - https://www.irs.gov/faqs/social-security-income/back-payments/back-payments