I just have this funny headcannon that the lasso of truth doesn't work on Dr. Doofenshmirts, only because he tells the truth a lot. He never lied because of either some f'd story about his childhood about lying or the fact that he didn't want to set a bad example for little Vanessa.
Like here's how the whole situation plays out. doof makes a machine to take over the tri-state area, perry the platypus stops him and destroys it, doof is blown away (cursing perry of course), and ends up on the island of the Amazonians (themyscira), gets captured and is taken to the queen and questioned and the whole conversation ends up being this:
Queen hippolyta: "who are you and why are you here!?"
Doof: "my name is Doctor Heinz doofenshmirts, I'm an evil scientist trying to take over the tri-state area. I got here because my arch nemesis, perry the platypus, destroyed my machine that was meant to turn all the newspapers soggy and wet. It blew up and now I'm here"
Queen hippolyta: "I don't believe you. Bring forth the lasso of truth"
*they get the lasso of truth and tie it around doof's hands*
Queen hippolyta: "I will ask you again, who are you and why are you here?"
Doof: " listen lady I just told you, my name is Doctor Heinz doofenshmirts, I'm an evil scientist trying to take over the tri-state area and I got here because my arch nemesis, perry the platypus, destroyed my machine that was meant to turn all the newspapers soggy and wet. It blew up and now I'm here. By the way this is some very pretty rope"
Queen hippolyta: "impossible, no mortal can resist the lasso of truth"
Doof: "I already told the truth. By the way how come you guys don't have any men around here, when your friends took me here I didn't see any other men around here, what happened?"
And then just doof ends up being watched to see why the lasso didn't work, and then he accidentally traumatizes them by talking about his messed up childhood but ends up giving them faith by his talks about how much he cares for his daughter