What is Due East?

[TacomaSailor]

I thought I understood a bit about long distance navigation but the following question/answer on “Who Wants to be a Millionaire” has me puzzled:

If you head due east from New York City where will you hit land?
- Ireland
- Lisbon
- Senegal
- Norway


Heading Due East to me says “stay on the same line of latitude” so my answer was Lisbon because NYC is at 40N and Lisbon is at 38N.

The TV show said the answer was Senegal, which is at 24N.

Using Visual Suite Bearing and Distance from NYC:
Lisbon is at a heading of 65T and Senegal is at a heading of 90T.

How can one stay on the same line of latitude (40N) and traverse a bearing of 65T?

How can one head Due East from 48N and end up at 24N?

What very fundamental fact of navigation am I missing?