The only things i've ever tossed into lava were a few duplicate maps that i made by accident. otherwise i save everything for current or potential future use.
regarding your afk fishing stuff:
if you make a grindstone, you can unenchant all the items that you consider junk, like the bows and fishing rods and stuff and collect the experience from them. you can use them as furnace fuel afterwards, or combine them with the grindstone for free to make complete bows and rods et.c with increased durability.
trade the rotten flesh with the village cleric for emeralds
combine the leather boots in the grindstone for free and make complete ones to enchant
lots of ways to do things...