Mama, it's OK to criticize. But, when you do, you really need to be telling the truth.
First, Cruz wasn't even on the sidelines in the Mississippi Affair. That was a Senate leadership show, McConnell's, conducted outside the bounds of the NRSC.
And, when Cruz discovered what had happened, by whom, he immediately resigned.
As to Lawrence v Texas, the SCOTUS took the case in December, 2002, they scheduled briefs in January, 2003 and oral arguments in March, 2003.
Cruz wasn't appointed Solicitor-General until February, 2003. Cruz could NOT have represented the state in Lawrence vs Texas.
As a Texan -- and as a conservative -- you should've known this.
Since he was appointed in February and the case heard in MARCH of that year, there is no reason that he couldn't have.