Are Lieutenant Governors elected or appointed?

Answer 1

This depends on where you are. In the US, the Lieutenant Governor of a state (in the 43 states that have one) is elected, either on the same ticket as the Governor, or independently, depending on the state.

In Canada, all (provincial) Lieutenant Governors are appointed by the (federal) Governor General on the advice of the federal Prime Minister and in consultation with the provincial Premier.

In Australia, the federal lieutenant Governor is the longest serving state Governor. State lieutenant Governors are appointed, but in some states coincide with the state's Chief Justice of the Supreme Court.

In the British Crown Dependencies of Guernsey, Jersey, and the Isle of Man, the Lieutenant Governor is appointed by the British Crown. Historically, the Lieutenant Governor was recommended to the Crown by the British Ministry. However, in both Jersey and Guernsey, this will be changed to a recommendation by a local panel instead.

Note that the role of a Lieutenant Governor varies greatly from place to place, with the only commonality being their titles.