When we say "army" do you mean the entire US military or specifically the Army? Otherwise the Navy could handle it pretty well since lions wont swim out to the ships.
I meant just Army, but Navy is an interesting idea. They could definitely just shell the lions from a few hundred feet offshore, but they would run out of ammo eventually. And they would also run out of supplies, like food/etc. They'd have to dock, and when they did, the lions would be waiting.
the US army has tanks though and no amount of lions can pierce armor....the tank driver might run out of fuel but all he has to do is wait inside. then it becomes a waiting game as the lions start to starve and eat each other. eventually all the lions will die and the tank operators will still be inside their tanks with provisions.
u.s army wins
But if the lions were eating each other, there would still be plenty of lions. And even half of them ate the other half, there would be 50 trillion. I don't know how much food an average tank carries, but I doubt it is more than a few days worth. They'd have to get out to get water pretty soon after, too. And when they did... the lions would be waiting.