Is it possible to make a semi competitive deck with 2x Core Sets and the Lannister and Targaryen boxes?

It depends on what you mean by "semi competitive"…

Could you win some games against friends around the kitchen table? Probably.

Will you place in the single digits at a decent sized regionals or other major tournament? No.

Well, I would say give it a try. It certainly won't be as efficient as decks drawing from the most efficient cards in the entire cardpool, but you definitely have a good base for a decent PbtT deck for joust. Also you could make a decent Targ HttIT melee deck (without the power grab events from either KotSea or KotStorm it won't be as good as it could be though.)

Even more than what this guy is looking for, is it possible to make balanced decks with just the cards from the core sets and the expansions (no chapter packs)? I'm NOT going to be playing them in tournaments, but just want fair games with buddies. Thanks.