In a medium saucepan, cover potatoes with 2 inches salted water. Bring to a boil; reduce to a rapid simmer and cook until potatoes are tender
but not falling apart, 15 minutes. Drain potatoes and set them in strainer over pot to dry.
In a large nonstick skillet, heat vegetable oil over medium-high. Add one-third the potatoes to pan and shake pan
to arrange potatoes in one layer. Cook potatoes, without stirring, until crisp and golden on one side, then gently turn and cook until golden on all sides, 6 to 8 minutes total. Using a slotted spoon,
transfer to paper towels to drain. Repeat twice with remaining potatoes, adding 2 tablespoons oil for each batch.
Add a 1/2 lemon, thinly sliced,
to skillet. Cook until slices are golden on both sides, about 2 minutes.
To serve, season potatoes and lemon slices with coarse salt and ground pepper and squeeze fresh juice of remaining 1/2 lemon over top.
Good with steak, roasted lamb, or seared fish.