In Texas, the lieutenant governor
1.is appointed by the governor and succeeds the governor should the office be vacated.
2.is elected jointly with the governor and therefore succeeds the governor should the office be vacated.
3.is elected by the Senate and thus can succeed the governor should the office be vacated.
4.is elected separately from the governor but succeeds the governor should the office be vacated.
5.is appointed by the governor and thus cannot succeed the governor should the office be vacated.