There is no law that explicitly prohibits Texas public officials from offering a reward for a legal act such as providing evidence of voter fraud.
Texas Lt. Gov. Dan Patrick was within his legal rights to offer a reward for information about the November general election, and to make it as large as he wants. Patrick is not coordinating his activity with a campaign and is therefore not subject to political contribution limits.
The legality of the reward offer is contingent upon it being paid out from Patrick's private earnings. Texas's election code restricts the use of campaign funds for "personal use," which is defined as "a use that primarily furthers individual or family purposes not connected with the performance of duties or activities as a candidate for or holder of a public office."