All ok.
All similar meaning.
(1) While he was eating, I asked him to lend me twenty pounds. == He will want the money back one day.
(2) While he was eating, I asked him for twenty pounds. == No idea of the terms/arrangement
(3) While he was eating, I wanted him to lend me twenty pounds. == You thought it. You may or may not have told him.
(4) While he was eating, I asked for twenty pounds from him = = No idea of the terms/arrangement
(2) & (4) are basically equivalent.