In a statewide election, which is separate from the Governor election. This means it is possible for the Governor and Lieutenant Governor to be from separate parties, which last happened during George W. Bush's first term.
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The Lieutenant governor of Texas, is selected by state wide election although, the Texas Senate also has the constitutional power to replace a lieutenant governor in the event of death, resignation or election to higher office.
[snip] In the case of a vacancy in the Lieutenant Governor's office, the Senate elects one of its members to act as President of the Senate until the next statewide office election, in effect becoming the Lieutenant Governor. A Senator elected as presiding officer in this way retains his district seat and the voting privileges entailed with his Senate election. --EN. WIKI.
With the election of Texas governor George Bush to the US presidency, Lieutenant Governor Rick Perry became governor of Texas on December 21, 2000. His successor, was Bill Ratliff, appointed by the Texas Senate to fill the vacancy. Ratliff, served the remainder of Perry's term, through 2002. David Dewhurst was elected lieutenant governor in November 2002, when he defeated former Democratic Comptroller John Sharp of Victoria. Dewherst, was reelected in 2006, and is the current [as of 2009] lieutenant governor of Texas.
see also: http://en.wikipedia.org/wiki/Lieutenant_Governor_of_Texas
The lieutenant governor of Texas is chosen by general election. The lieutenant governor is on the same ballot of the governor.
The Lieutenant Governor presides over the State Senate with a few exceptions.
lieutenant governor
Jake Sullivan
lieutenant governor
John Houston, Governor of Texas.