(Corrects paragraph 22 to show Lake was an anchor for a local Fox affiliate, not Fox News) By Ted Hesson and Alexandra Ulmer WASHINGTON (Reuters) – In the past year, Texas Governor Greg Abbott has deployed thousands of National Guard troops to the southern U.S. border, begun building a new border barrier, and arrested migrants for allegedly trespassing on private property. The two-term Republican governor has taken the lead in opposing Democratic President Joe Biden’s immigration reforms, earning him an endorsement by former President Donald Trump. But as Abbott runs for a third term, conserva…