According to Oxford Dictionaries, "lose face" means:
Be humiliated or come to be less highly respected
And esteem, honour, and respect were given as synonyms. They seem contradictory to me if not outright opposite.
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The synonyms given are for 'face', in the expression 'lose face'. If you lose it, you lose those things.
Definition of lose face in English:
Be humiliated or come to be less highly respected.
‘the code of conduct required that he strike back or lose face’
respect, honour, esteem, regard, admiration, approbation, acclaim, approval, favour, appreciation, popularity, estimation, veneration, awe, reverence, deference, recognition, prestige, standing, status, dignity, glory, kudos, cachet, image