"Lucked out" came into the North American vernacular in the hippy days of the 1960s-70s. (And I do mean 'hippy,' not 'happy.'
) It was just another way of saying "got lucky." What the provenance is, I have no clue. ("I have no clue" also became popular at about the same time.) "Lucked out" became so common an expression that these days it's not even considered slang any more, although one hears it a lot less than was the case back in those halcyon days.
As to filling in and filling out -- British politicos "stand" for office, while Americans "run" for office. I never figured that one out either. And, as with your example, McT, that's not really a peeve.