Since I'm going to have a say in what gets slated at the end of this, I'm going to post my positions on existing favorite types in addition to the ones jas61292 mentioned, although I'm definitely going to focus on what jas61292 is directing the discussion towards.
It's pretty clear that Aegislash and Fairies are our top targets, but the former is much, much more difficult to deal with than the latter. However, Aegislash is something that can be dealt with during stages other than Typing (i.e., Typing is not the only stage where we can deal with Aegislash, although we definitely have to pay it mind right now). Fairy-type Pokemon, however, cannot be handled well without a typing that takes advantage of common Fairies or a ridiculous defensive presence.Most Fairy-type Pokemon are powerful. Really powerful. The top-used Fairy in OU, Azumarill, is a Physical powerhouse. Other Fairies such as Sylveon and Mega Mawile are not fun to take hits from. Our core is absolutely manhandled by Fairy-type Pokemon at the moment unless Lucario runs the incredibly unreliable Iron Tail, so we're going to have to address the Fairy problem here and now. Since we're building an offensive core with Lucario and Latias, it's at least as important to maintain our offensive presence as our defensive presence. As a result, I believe Dark/Poison is the best typing available to us at the moment because we get one powerful STAB in addition to a sneaky good defensive typing in Poison. Dark/Poison is preferable to other choices such as Poison/Steel and Normal/Ghost because it gives us enough insurance against Aegislash and Fairies while actually threatening them back. Furthermore, it doesn't compound our weaknesses to Conkeldurr, as we are not weak to its STAB and resist Knock Off. We'll have a problem with Grounds as well, but it won't be difficult to pair this core with something like Landorus-Therian that can provide additional insurance in addition to Latias.
Poison/Electric gives us a Fairy resistance and a means to hit Fairies super-effectively, but I'm not particularly sold on what the Electric typing does here. It gives us an extra Zapdos check, but we've already got Latias in this core. It's not checking Mega Pinsir without at least 105+ Speed and maximum investment, and even then Flying spam is not really that important of a strategy to counter. Lucario's +2 ExtremeSpeed does pretty well against Talonflame and Mega Pinsir, and at the very worst Lucario's breaking even against Talonflame and causing a double KO. When the worst-case scenario against Talonflame and Mega Pinsir is that you break even or heavily cripple them, I'm not sure why we need to devote one of our two types to defeating it. I find this typing outclassed by Dark/Poison, which can take Knock Offs and doesn't fall into the "
Normal/Fire hits the "threaten Aegislash and Fairy-type Pokemon" benchmark, but provides us essentially nothing beyond that. We're walled hard by Heatran and have no recourse against Conkeldurr at all. If Conkeldurr comes in against this Pokemon, we will not be able to handle it with our core. We also have no chance against Azumarill, who shatters us with an Aqua Jet or Waterfall. Although some of the other typings don't do particularly well against Azumarill, this one does by far the worst and essentially mandates that we'll need additional Pokemon to get through Azumarill as well as Conkeldurr. It also has potential issues with Landorus-Therian and Hippowdon. This isn't a bad typing for what we want to do, but this is a typing intended to hard-counter our threats and little else.
I'll edit this post or possibly post again with some more typings, but these are my thoughts about some of the current contenders.
You start perfectly by saying how checking Fairies with typing is more important than checking Aegislash with typing, and then you say that you favor Dark / Poison, which is neutral to Fairy moves and thus can't really switch into them without ridiculous physical bulk. Also, you say that with this typing we fare well against Conkeldurr, which is not even a big threat to our core, as the only Pokemon it can threaten 1 v 1 is Lucario, and it can't switch into anything. Finally, you say that flying spam is not such an important strategy to counter, when Mega Pinsir is an S and Talonflame an A+ threat in the viability ranking list, and together they form one of the best offensive combos in OU. Not only this, but Talonflame has the speed advantage and will always play first against our whole core, except from Lucario, which can sacrifice itself to weaken it with ES, but isn't the point to assist Lucario's sweep, and not to sacrifice Lucario in order to deal with Talonflame? Yeah, Lucario might get to +2 before Talonflame enters the field, but Talonflame getting into the field before Lucario sets up is way more likely, as Lucario is a late game sweeper, where Talonflame can work great throughout the whole game.
With that said, i see a lot of support for typings such as Ghost / Normal and Dark / Poison, which have a clear focus of being able to switch into Aegislash but not much else, so let me say this: Aegislash is not that hardest Pokemon to check, even without resisting Shadow Ball. Garchomp, specially defensive Heatran, Landorus-T, and Assault Vest Excadrill all do it just fine, and none of them resist Shadow Ball. On the other hand, let's see how many Pokemon check or counter Azumarill and Mega Mawile without resisting Fairy moves: Rotom-W and Landorus-T. That's it. Landorus-T can only check Mega Mawile, as Azumarill can fuck it up with Waterfall, but it can at least take a couple of Play Rough hits. And Rotom-W can only really check CB Azumarill and Mega Mawile once if they go for Play Rough, which they will as our core does nothing to discourage this so far, and Rotom-W needs max HP / max Def+ to do so, max HP gets OHKOed by both after SR. So, in order to check Fairy-types, we will need physical bulk to the level of Landorus-T, or just good physical bulk (Rotom-W) with max physical bulk investment, which goes against what we agreed, to build a Pokemon able to apply offensive pressure, and not a defensive pivot. This is why a Fairy resistance is a must, not a Ghost resistance.
And, because right now, Talonflame can go to town with just spamming Brave Bird, i think that a Flying resistance is really important as well, but not an absolute must like the Fairy resistance. So far, here are the typings that resist both Flying and Fairy, are not weak to Aegislash's common moves, and their STABs provide decent offensive presence:
Electric / Poison: Resists Fairy without being weak to any move that Fairies commonly carry, outside of Mega Gardevoir's Psyshock. Also, resists Flying moves while not being weak to Flare Blitz or U-turn, which is excellent. It also resists Iron Head, Sacred Sword, Flash Cannon, and is immune to Toxic, all moves that Aegislash can carry, so we only have to worry about tanking Shadow Ball. Electric / Poison is weak to Psychic and Ground, both of which Latias resists, while Electric / Poison can take on Steel and Fairy-types for Latias, so those two have good synergy together, which is good, as Lucario and Latias don't have many reasons to be used together, so we will have to make sure that the CAP pairs well with Latias if we want people to use Latias in this core. Moving on, Electric is a good offensive STAB, and Poison helps hit most Grass- and Dragon-types at least neutrally, outside of Ferrothorn, which is nice. However, the combo is completely ineffective against Ground-types, which are already somewhat problematic to our core. However, all typings have flaws, and this flaw is not that hard to solve with stats and the right movepool, so i think that this typing is one of the best proposed so far.
Electric / Fire: Resists Fairy moves but is weak to Azumarill's Water STAB, and resists the whole moveset of Talonflame. Also, it's not weak to any of the moves that Aegislash carries and can threaten back with Fire STAB. Fire / Electric has great synergy with Latias, with Latias resisting Water and being immune to Ground, and Fire / Electric dealing with Steel and Fairy-types, not to mention Latias getting rid of SR, which CAP is weak to, so this is a big plus. Finally, Fire / Electric is fantastic neutral and super effective coverage, with only Garchomp, Latios, and Latias resisting both, out of which Garchomp can be dealt with by WoW, a move that all Fire-types carry. As for the cons, Fire / Electric is weak to Ground, which makes Pokemon such as Scarf Excadrill and Garchomp even more problematic to our core. Also, being weak to Water while you want to check Azumarill sucks, but at least we resist both of Azumarill's STABs without our core, so we can play around choiced versions and revenge kill BD sets with Latias. Not the best solution, but a solution nonetheless. All around, pretty good typing though, with many pros and little cons, which can be addressed later in the concept. And no, we won't make Rotom-H v2 with this typing, we have a ton of options to make it different, such as different ability, physical orientation, set moves, different stat spread, etc. There are plenty of ways to go with an offensive Fire / Electric type, so don't let Rotom-H discourage you from picking Electric / Fire.