To dawdle over a beverage (usually at a restaurant), talking, for an inordinate period of time, sometimes getting refills. Can be extended logically to mean taking a long time to finish anything that would be expected to take a much shorter length of time. Originally used by a friend of Lothie's to explain why a short meal turned into hours when Lothie was present, usually because she was still lingering over her coffee.
No, we can't leave -- I'm still lothie-ing my coffee!" "Mike lothied over his spreadsheet for so long that he didn't get it submitted in time for the sales meeting.