You sound like the dream seller!
AFAIK its more convention than law, but typically vendors get a prorata amount of their LPT refunded depending on the closing date. This should come to you via your solicitor with the rest of the funds I believe. I've never sold but I know as a buyer I twice paid this sum when transferring all the money owed into my solicitors client account.
The annoying thing though and something that might be useful for someone else to know is we also had to pay our 2019 property tax too. It gets deducted from our salary every month but according to revenue it is not transferred to the LPT department until the end of the year. So it would appear as if we hadn't paid it for paperwork. So we had to pay it and then we will have to claim back what we had paid already in January.
Just one more thing to think about!