The correct option is B he doesn't
In reported speech, the word order and pronouns will be different from
the original speech, because the speaker has changed. Accordingly, the
tense will also change, in most cases.
The simple present tense in direct speech usually changes to simple past tense in the reported form.
It
isn't always necessary to change the tense. The given speech states a truth "I don't tell a lie" which still holds true. Hence the
tense remains as present simple.
Option C: 'He doesn't' is in the
present simple, the subject 'I' has changed to 'he' as the narrator has
changed. Hence C is the correct option.
Option A: The verb 'don't' in 'he don't' must change in person (third person point of view) as the subject has also changed in person (from first to third). Hence A is incorrect.
Option B: 'He did not' is in the simple past tense. It suggests that an event has happened in the past. But, 'I don't tell a lie' is a truth, not a particular event. Hence the tense does not
change to past. So, option B
is incorrect. (did not is an expansion of didn't)
Option D: The subject and verb changes in
reported speech. 'I' will change to 'he' as the narrator has changed.
('he' refers to Evans)
Hence option D is incorrect.