Put the crayfish in the sink under cold running water to make sure they are alive. Discard any that do not move.
In a large pot, combine 2 gallons cold water, the salt, sugar, beer, and dill and bring to a boil over high heat. Add the crayfish, return to a boil, and turn off the heat. Let stand for an hour or two before serving.
Drain the crayfish and arrange on a large serving platter. Garnish with dill and squeeze some lemon juice over them.
Crack open the shells at the table and carefully remove the crayfish meat. Place the meat on white bread spread with mayonnaise, or eat it just as it is, with a drop of lemon juice. The white meat in the tail is the best, but the meat from the head is also delicious; do not eat the papery gills.