Iron Golem Farm not Dropping Iron Ingots

The Iron Golem should drop 3-5 iron and 0-2 roses. The lava could be burning the iron and not the roses because the drops get launched at different angles. I would suggest you try this multiple times to make sure your results are valid.

You may have to kill them by hand. Apparently there's a bug or change that makes mobs not drop the same stuff when they die as when they're killed personally, e.g., zombies won't drop iron unless you dispatch them personally, but only in SMP.

You might be able to change out the lava for a piston-based suffocator, timed so that it takes a fresh bunch of golems down to as few hearts as possible, then kill them by hand.

One reason the golems may not be dropping iron ingots is because you have to kill them yourself, kind of like XP, if you don't kill the mob, it wont drop XP. In this case, it's iron. Mojang probably did this to slow down or stop automatic iron farms. But you still can have a farm, just take out the lava, make it so you are out of their hitting range but they are in your range and make a room (if you don't have one already) where they will "wait" to be killed. They don't drown either by the way. You could use your huge amount of cobblestone from mining to make swords that you would specifically use for your iron farm.

Reducing their HP (I haven't tested this yet though)

You could take that lava and use it for the the same purpose but wont kill them you could make it where they fall through a 1 block (or 2) layer of lava before reaching the "waiting" room (if you did what I said above) this could reduce their HP enough to take only a few hits with a sword.