Rinse the asparagus and trim or snap off the tough end of each spear.
Place the asparagus, coconut oil, and garlic powder in a zip-top plastic bag, seal, and shake lightly to coat the asparagus.
In a bowl, mix the Parmesan cheese, mayonnaise, and pressed garlic.
Lay out 4 rectangular pieces of parchment paper, large enough to fit the asparagus and fish with plenty of paper remaining on the sides and ends to fold into packets and seal. Divide the seasoned asparagus evenly among the sheets of parchment.
Place the fillets on top of the asparagus, skin side down. Top the salmon with the mayonnaise mixture.
Fold the parchment paper over the fish and seal on all sides. The packet should look like a calzone.
Place the packets on a rimmed baking sheet and bake for 12 to 15 minutes, until the internal temperature of the salmon reaches 145°F (63°C).
Garnish with fresh dill and lemon slices, if desired.