I know this is kind of old, so I hope this doesn't seem like necroposting, but I have some experience here.
Lithium batteries slip by all the time in checked baggage, but they aren't supposed to be there. Only in carryon, and you should expect secondary screening.
As far as the airsoft replica is concerned, the best practice is to check it in like a firearm. Put all of the airsoft stuff (replicas, empty magazines, beebees, etc) into a single case, if possible, that can be locked with a TSA approved padlock. Remember to remove the lithium batteries from optics, lights, etc. Take the case to the check in, and declare it. Expect to be patient; many adults do not know what 'airsoft' means, but they DEFINATELY know what a 'gun' looks like, orange tips or not.
If you just toss it in a bag or whatever, that shape is going to show up on the bag scanner, and that bag is going to be tossed. Especially a large mass of beebees. Several people will stand around it and try to figure out what's going on there. Airport police and the screening manager may get involved. You might get called back to explain what you're doing with a machine gun.
And, pitch all your gas containers. CO2 capsules, green gas canisters. Make sure your grenades and mags are downloaded. Those are definately no go's and can only cause you grief if they decide it's time to hammer someone.
Lastly, zero pyro. No smoke, no poppers.
If I had to travel now with airsoft, I might even make a sheet to put in with the replicas that explain what airsoft is, and a website for more info.