For the life of me, I could not figure out what they wanted me to mine? When I arrived, there was only the broken asteroid, and the barren asteroid, and the mining site, no Lavite?
add kernite to your overveiw, it should be somewhere around the broken crystaline asteroid, you can also find it with a survey scanner, about 17-14km from the warp in point
They spawn in at 45-50Km