As far as I know, the only way to trap them is to filter them with a water trap (zombies fall to death or into lava, chicken don't die and get swept away by water as they float.
At the bottom of the drop, you could have a 1-high gap on one side. They'll go in and suffocate.
You could either have it at the front so they head towards you where you're killing the others, or - if that is awkward - you could attract them in a different direction by putting a villager on the other side. They'll head straight towards a villager rather than the player, unless you hit them.
And it's reasonably easy to get a villager in a zombie spawner area, by curing 1 zomb villager.
If you're not keen on the auto-suffocate idea, you could put a piece of cactus in there, but watch it because cactus (or the lava you mentioned) will destroy at least some drops. So just letting it suffocate itself is probably easier.
I don't think it'll cause much of an issue though, because they only seem to spawn about 1 time in 1000.
EDIT: PS, another option that I've used in the past, if you are just killing everything for drops and not looking for XP, is put an iron golem in the bottom to kill any that survive the drop.
The Darkness will win one day, and light's time being the winner is nearing it's end. Because light is overrated.
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Why would a fast zombie need to ride a slow, passive chicken?
Chickens are evil. Oh believe me, they are evil. The next thing you know they will be hiding inside your chest, meddling with your sword, until they hear you coming back, and then they prepare themselves for vengeance of their fallen brothers...