'Which is the correct sentence?'
The only correct sentence is the first one: 'I never lose hope'.
In this sentence, 'hope' is an abstract noun. Unlike in Spanish, English abstract nouns ( like love, hate, courage, happiness, despair and so on) do not have an article when referred to in general terms. This is why 'I never lose the hope' is wrong. 'The hope' would mean one particular hope, not the feeling of hope in general.
'I never lose to hope' makes no sense at all. You can never put 'to' or a verb after 'lose'.