Yes they do. Whether it's just show prize winnings, or both production budget and prize fund not sure.
The Irish lottery 'lucky star' logo is all over the show on screen, although they don't have a pre-titles or pre/post ad break sponsorship bumpers with the lotto logo.
I think RTE funds the production of Winning Streak with a little bit of help from the Irish Lottery, all prize money is provided by the Lottery and not RTE.
To enter you have to match three stars on a Winning Streak scratchcard, and if you do, you write your name and address on the back of the card, and put it into a special envelope available at lottery outlets and post offices, and post it to the lottery HQ.
Each week 5 names are drawn by the hosts from a random drum of 100 cards sent in, they appear on the following week's show. Must be a bit of a rushed week for the contestants, especially after getting over the shock of knowing they will appear the following week on national television, and organising 20 or so of their family and friends to come to RTE Studio 1 for the recording.