If you plan on using your own urine for ferts, you’ll need to dilute it by 10 to 1. There is entirely too much nitrogen in urine to use straight. Urine contains an average NPK of 11g N - 1g P - 2g K per litre.
You can use any soilless medium you want and add volcanic rock to it and it’ll work just fine. If you’re only adding lava rock to increase soil aeration and decrease soil compaction, perlite or vermiculite work to accomplish the same thing and weigh a whole lot less than lava rock.