I will alch all of runite limps and OSRS gold
daggers. Recall avies addy pubs are too common and limps and daggers aren't too common while irons drops are many of these rares and even some such as vissies are excessively rare but it worth wayy a whole lot more than avies common drops.
Personally, I'd recommend the Karamja dungeon, only outside of this Tz-Haar area. There's a whole slew of alternatives for this one; You could melee them at that point, utilizing a normal weapon, food plus a bunyip if you're able to. Or you might halberd them from a safe spot, or use array from a secure spot, which makes it food free. Or there's the option of a cannon that you may try either on it's own, or even with the mixture of some of the above mentioned. Obviously, there are different areas, though I would recommend this area for sure.
Just realised the title says greaters, but the post says lessers. If the task is really greaters, then my only recommendation is the dungeon in brimhaven. You can use any of the aforementioned options, though you need to contend with all the terror dogs too. Regrettably, there are not a range of great possibilities for greaters (no pun intended), however, you only have to soldier on whether it is those.
Inventory: Range gear for buy RS gold
Ahrim (such as rune xbow). Easy teleport into an altar (Ardy Cloak, House teleport). Spade. 4 Prayer Potions. Monkfish.