What a strange expression “hang in there” is! It’s definitely American. A funny thing has happened to it recently. It has got mixed up, understandably, with the British expression “hang on”, meaning to wait for some eventuality or other – I assume it derives from the use of the telephone; compare “to hang up” which used to mean simply to place on a hook, as for example a picture on a wall, and became another telephone-related phrase meaning to terminate a telephone call by replacing the receiver.
Even highly literate writers are caught out by the interlocking permutations of the two verbs ‘to lay’ and ‘to lie’.