Iron Golem Farm not Dropping Iron Ingots

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.

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.