Lose face - Save face
Lose face - Be humiliated; lose one's reputation.
'Lose face' began life in English as a translation of the Chinese phrase 'tiu lien'. That phrase may also be expressed in English as 'to suffer public disgrace', i.e. to be unable to show one's face in public. In 1876, the consular official Sir Robert Hart published a series of essays - These from Land of Sinim - Essays on the Chinese question which included this observation:
"The country [China] begins to feel that Government consented to arrangements by which China has lost face; the officials have long been conscious that they are becoming ridiculous in the eyes of the people."
Hart was well-regarded in both Britain and China. In addition to his baronetcy he was awarded the CMG, KCMG, and GCMG. China honoured him with several high status awards, including the title of grand guardian of the heir apparent, an honour never before (or after) bestowed on a foreigner.
'Save face' comes later. It has no direct equivalent in Chinese and is merely the converse of 'lose face'. The first known record of it in print is in the June 1899 edition of The Harmsworth Magazine:
"That will save my face in the City."