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

No. The gap stays at 8h all year.

When is the best time to call Seoul from Lagos?

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

Lagos is 8h behind Seoul. This gap is the same all year — neither city shifts its clocks relative to the other.

Lagos

Nigeria

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Seoul

South Korea

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

City	Time zone	UTC offset
Lagos · Nigeria	Africa/Lagos	UTC+1
Seoul · South Korea	Asia/Seoul	UTC+9

What is the time difference between Lagos and Seoul?: Lagos is 8h behind Seoul. This gap is the same all year — neither city shifts its clocks relative to the other.
Does the time difference between Lagos and Seoul change during the year?: No. The gap stays at 8h all year.
When is the best time to call Seoul from Lagos?: There is no overlap between standard working days, so one side has to call early or late.