The Lt. Governor in Texas is more powerful than the Governor, actually.
I think this is more of a traditional claim.
Texas has a fairly weak executive branch, with independently elected executive officials (Attorney General, Comptroller, Ag Commissioner, Land Commissioner, Railroad Commissioner, judges, etc.). The governor doesn't get to act as commander-in-chief very often.
Ordinarily, the legislature only meets every two years, and the time of meeting is limited. Traditionally, the Senate and the House have deferred to the Lieutenant Governor and House Speaker to control what legislation is considered. The House Speaker is elected by the members, so he has to concede power to committee chairmen in order to get elected.
