Cut salmon into two equal pieces and make sure pin bones are removed. Line a rimmed pan with plastic wrap and place salmon side-by-side on plastic wrap.
Mix together sugar and salt and sprinkle evenly over both salmon pieces.
Lay lemon slices across the salmon, then arrange dill, thick stems removed, on top.
Lift up one end of the plastic wrap and fold over salmon to sandwich it onto the other half. Wrap salmon tightly.
Place in the refrigerator, preferably with a heavy container placed on top of the salmon to help extract the liquid.
Let rest for 48 hours, then remove from refrigerator and unwrap carefully, minding the juices that will leak out.
Discard the dill and lemon and slice the gravlax thinly with a very sharp knife.
Store in the refrigerator in an airtight container for up to 5 days.