I agree with you that the two options you presented are not equally unsuitable or unattainable. The first option, to lose the ability to lie, is a difficult but achievable goal, while the second option, to believe everything you're ever told, is simply not possible.
If I were given the choice, I would definitely choose to lose the ability to lie. I think it would be a very liberating experience to be able to tell the truth, even when it's difficult. I would also feel more confident in my relationships, knowing that I could always be honest with the people I care about.
I chose the same thing but I don't see a good coexistence between someone who only tells the truth and those who mix the truth with "necessary" lies.