Would you agree Joker would get the Death Penalty if he was on trial in a Texas Court?

Yes. I think an argument could be made that the Joker is not really insane but is very much aware that what he is doing is wrong. And even if he is insane it would still be in the best interest of society in general to have him executed. Clearly he is beyond reform and keeping him locked up only risks lives because he is so adept at escaping. There might be the odd person who would protest a death sentence based on the Joker's mental state. But I don't think too many people would mind.