I don't need to. One of LPUSA's biggest weak points is foreign policy and national defense.
For instance, suppose Hitler had conquered all of Europe, then Canada and Mexico, and began moving troops into those two latter countries—all while striving to develop the A-bomb, of course.
If you're America, do you honestly wait for Hitler's army to attack first? Or develop and use an A-bomb? Ludicrous. At some point—hopefully early on, before it's too late—you preempt that totalitarian piece of sh-t and destroy his capability to conduct aggression.
The LPUSA's hyper-dovish attitude with respect to national defense is their weakest issue. Fortunately, the vast majority of the country would never be so naive, so it would be unlikely to be an issue if the LPUSA somehow magically controlled the federal government. When the People want war—and often when they don't—they get war.
But as far as domestic policy and limited government, the LPUSA would be exemplary. Just review those aspects of their platform. You certainly won't find much "socialism" in a party that wants to abolish things like the Progressive Income Tax, Obamacare, Social(ist) Security, Medicaire, and Medicaid, to name only a few...
Explain the nominee they had for president. That is the direction that party is going.