Don’t know about the Weimar Republic situation (without looking it up atm, best I know is that it was just really corrupt and ineffective), but what I think I know about Lebanon is that they have one PM or at least representative for Christians, one for Sunni, and one for Shia, or maybe it’s on a rotating basis. Given how the religious makeup is nowhere close to what led Lebanon to its situation, I don’t see that happening to the US.
As for a military coup, I suppose if you wait long enough, it could happen, but the military culture needs to be amenable to a coup, which we’ve been careful about. More likely it’ll happen via some bloodless means such as section four of the 25th amendment. Then again on that one, they were imagining a much more dire scenario than an awake and screaming Trump, they made it as an answer to a what if Kennedy had managed to survive but was in a coma. It does read like a legalized coup, but made for a particularity dire and specific kind situation where you’d want the ability.
In actually looking at Wikipedia, the Weimar Republic failed in part due to that Germany had limited democratic traditions* at that point and the parties were hugely inexperienced when the government was formed. Though Wikipedia states that there are a whole host of reasons leading to its failure.