Here's the setup I use in my custom world:
Best angle I could get. The top has a relay fed by a Mk II chassis LP with a terminus module setup with the junk I no longer need. The relay then ejects down a cobble chute that has 2 air blocks. The items hit an obsidian pipe that sucks them up and directs them to a void pipe in less than a second.
This seems silly since I'm starting off with pipes but there's a huge problem, LP, like BC pipes and RP, drop into an inventory. So I can't have the void attached directly to the terminus. So I initially had a chest there to provide a valid inventory. I went through all the suggestions given above.
1: Chest to another LP extractor then to a void pipe. Didn't work because the LP attached to the chest wasn't attached to the network. No power, no extraction. Connecting it to the network forced the items to loop back to the terminus.
2: Chest w/wooden pipe and an autarchic gate attached to the wooden pipe. Yeah, I'm trying to dump the cruft that is coming off my quarry. It couldn't keep up with my quarry when it only had 2 hobbyist and 1 magmatic attached to it (7.6Mj) let alone when I dropped my RECell on the line.
3: Chest w/filter, structure pipe & basic gate attached. The structure pipe & gate were there to emit a redstone signal when empty. This stopped the timer on a 2s delay which would pulse to force the filter to pull a stack every 2 seconds. The filter then ejected into the chute/obisidian/void pipe. This was able to keep up with my quarry at full speed but the constant click, click, click, click was driving me batty!
4: LP pumping into relay which ejects down the chute. Faster than the above as it ejects items as soon as they appear, no timer needed. Which also means it is far quieter.
Why not into lava or cactus? For the exact reason why the void pipe was made, those solutions, while serviceable, are laggy as all hell when you stress the system. The void pipe is easier on the machine running the world.
Why not into a recycler? No IC2, no recycler.