I have always played where a new game gets a new "Jack for deal" scenario. Playing with my nephew this week he was ADAMANT that since he and his partner won the last GAME, this gave him the privilege of dealing first. I say a new game has absolutely NOTHING to do with previous games. Who is right?
I would have to agree with you. A previous game definitely has nothing to do with the proceeding game. It is equivalent to playing a game then a few years later the winner is still able to be the dealer without the blackjack deal (well maybe not quite that far, but you get the point). But just clarifying we are talking about entirely new games, not rounds? If we are talking about games then yes redo the blackjack deal.
You're likely to get different answers from different people/rulesets. For example, the rules at euchrelinks.com say:
I. To determine who the players will be in a euchre game, the cards need to be shuffled by one (potential) player, then passed to the right for a cut. The person who cuts should then deal one card face up to each person who wants to play, starting to their left and continuing clockwise. The player who receives the first jack will become the first dealer when the game begins. The cards should be dealt in this manner, skipping players who already have jacks, until all four bowers are dealt. The players with the same-colored jacks will be partners. Players that don't receive a jack must sit out.
This is similar to how many rules in euchre are chosen. With my friends, I play that anyone can go alone - whether you called it or not. If you defend alone and euchre the makers, your team gets 4 points. Most people don't play that way. Some people don't screw the dealer. I know of one variant where if the dealer calls it s/he must go alone. Most people I know play to 10, but some play to 11, and I've known some who play to 5 for quicker games.
When in doubt, I always say that house rules govern. If you're playing at your house, then dealer gets selected at random. If your nephew is hosting, you may have to play by his rules.
I play differently, or did long ago. When playing multiple games the winner gets the first deal.