The following answer was provided to Lacerte tax preparers asking the above question.

In this scenario, no.

After the taxpayer's death, quarterly estimated income tax payments are not required to be made for next year's return.  The date of death represents the end of the tax year for the deceased taxpayer and the next 1040 filed on behalf of the decedent is the final tax return and only income received up to the date of death is reported.  As a result, estimated tax payments are not required and not necessary. 

In Screen 1 of the Lacerte program, the following occurs when a Date of Death is entered:

Filing Status:                                      Forms Tab      

Single                                                   1040-ES is suppressed  (not bolded) under the Forms section

Married Filing Separately                 1040-ES is suppressed (not bolded) under the Forms section

Head of Household                           1040-ES is suppressed (not bolded) under the Forms section

Qualifying Widow(er)                        1040-ES is suppressed (not bolded) under the Forms section

Married Filing Jointly                         1040-ES will still appear bolded under Forms section since the surviving spouse may need to make estimated tax payments for her or his individual income tax liability.