Get your pasta boiling in generously salted water
Meanwhile, remove the tough ends of the asparagus and then cut in pieces according to the shape of the pasta. Ex: small rounds for small shapes, ribbons for long pasta
Add 1T olive oil to a skillet on medium low heat, and when the pasta is almost cooked (still slightly tough in the middle) add it to the pan along with a splash of cooking water. Add the chopped asparagus and zest of half the lemon, mix.
Keep tossing the pasta in the pan until the asparagus is cooked. It should be soft but still have a slight bite. If the pan begins to seem dry, add a splash of pasta water to loosen the sauce
Turn off the heat, add juice of half the lemon, mix. Add the butter and mix again, then grate over the pecorino and mix again. Taste and add salt or extra lemon if needed.
