Does the time difference between Lagos and Vancouver change during the year?

Yes. Because of daylight saving time the gap moves between +8h and +9h.

When is the best time to call Vancouver from Lagos?

There is no overlap between standard working days, so one side has to call early or late.

Lagos is 8h ahead of Vancouver. This gap is not fixed: daylight saving time moves it between +8h and +9h during the year.

Lagos

Nigeria

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Vancouver

Canada

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A 9-to-5 working day in Lagos does not overlap one in Vancouver at all — somebody has to take the call outside office hours.

City	Time zone	UTC offset
Lagos · Nigeria	Africa/Lagos	UTC+1
Vancouver · Canada	America/Vancouver	UTC−7

What is the time difference between Lagos and Vancouver?: Lagos is 8h ahead of Vancouver. This gap is not fixed: daylight saving time moves it between +8h and +9h during the year.
Does the time difference between Lagos and Vancouver change during the year?: Yes. Because of daylight saving time the gap moves between +8h and +9h.
When is the best time to call Vancouver from Lagos?: There is no overlap between standard working days, so one side has to call early or late.