Strictly speaking, no, its the PPS number of the deceased or the deceased's estate that is required for Stamp Duty and LPT
But its not really a big issue, is it, being asked to provide it?
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From Revenue
Tax Reference Numbers & Fiduciary Capacity
Capacity Vendor/Purchaser details required
Personal Representative (Executor/Administrator)
Name and Tax Reference Number of the deceased or the deceased’s estate (where assigned a separate Tax Reference Number)