OOC: I was thinking that Franco Lopez had been a different person, and had pursued a different strategy before the war... Maybe choosing a friendly candidate in Bolivia prior to the interal issues and backing him up succesfully, and Chile resolving its war with Spain somewhat earlier.
OK, I'll go with that.
I don't think he would have thought alone, since he stood absolutely no chance of winning. He might have thought aginst Argentina if he was assured that Brazil would remained neutral (and secrety allied with him). he might have even attempt to fight Brazil alone if he had Uruguay and Argentina on his side (even if as informal allies). But since Brazil and Argentina where toghether, he would never have attecked. He only did so because he had Chile and Bolivia on his side, and he knew that would be enough to keep Argentina out of the war, at least in practice.
Yeah, I didn't think that the Paraguayan leadership would risk it either, unless we specifically made Lopez a megalomaniac, but that's frankly Out of This World.
Considering how the Paraguayans performed during the war, I think they could have a chance of winning alone, but that would depends on breaking the alliance between Brazil and Argentina (nothing the diplomatic genious that Lopez was couldn't do). Even IOTL he tried to get the support of Chile and Bolivia exactly to try to make Argentina give up the fight and avoid Brazil advancing through Argentine territory to reach Paraguay. If he is alone, maybe he would try to declare war only against Brazil while making negotiations with the Argentines, or the contrary.
However, as that would result in something a bit similar to OTL, I prefer the idea of Paraguay losing. Even if Paraguay had won alone, the reasons that created later the "Guerra Grande", or "South American War", or "Deserts' War", as you prefer to call it would still be there. With a Paraguay that had lost the conflict of the 1860's that conflict wouldn't happen, maybe only as a exclusively Pacific war.
For my country, if we had won the war with Paraguay maybe we would still be living under an Empire, as the roots of the monarchy's fall can be traced from that defeat. Also, with a winner Army we wouldn't have dissatisfied officers trying to get more political power to the Armed Forces. So, even if a Republic is eventually proclaimed, probably we would be spared from the military dictatorships and the political unrest that plagued us during the late 19th century and early 20th.