To prepare the doughnuts:
Mix the batter ingredients in order with a wooden spoon, being careful not to overmix. You can place the batter in the refrigerator at this point and keep it there till you’re ready to fry, up to 48 hours. You may have to increase the frying time slightly to compensate for the colder batter.
Heat the oil in a large saucepan to 325 degrees. Drop the batter by small ice-cream-scoopfuls or teaspoonfuls into the oil and deep-fry for 3 minutes, turning the doughnuts often till golden brown on each side. Break the first doughnut open to check that it is cooked all the way through.
Drain the doughnuts on paper towels or a brown paper bag and sprinkle heavily with powdered/confectioners sugar, or place them in a resealable bag of powdered/confectioners sugar and shake them well to coat. Serve in a bowl or on a platter with a side of the lemon cream as a dipping sauce.
To prepare the lemon cream dipping sauce:
Bring about 2 inches of water to a simmer in a large saucepan. In the bowl of a mixer fitted with a whisk attachment (or using a hand mixer), whip the eggs and sugar together until very light yellow and fluffy. Mix in the lemon juice and lemon zest. Rest the mixing bowl in the saucepan, with the bowl’s base resting above - not in - the simmering water. (Pour out some water if necessary.) Cook, whisking occasionally, until the mixture is thickened and custardy, about 10 minutes.
Meanwhile, half-fill a large bowl with ice and cover with cold water. Remove the bowl with the custard in it from the saucepan and whisk in the butter until melted. Rest the bottom of the bowl in the ice bath and let it cool, folding the mixture occasionally to cool and thicken it.
In the bowl of a mixer fitted with a whisk attachment (or using a hand mixer), whip the cream until stiff. Fold it into the cooled lemon custard. Cover, and refrigerate until ready to serve. (The lemon cream can be kept refrigerated for up to 48 hours before use.)