ah, so you're talking geographically? Paraguay really only has one direction to go: south through Corrientes/Entre Rios and then paraguayan military can spread in multiple directions: through main part of Argentina (Buenos Aires and the northern provinces), to Uruguay, or to Brazil province of Rio Grande do Sul. From Paraguay itself, you can go north into Brazil, but that's a dead end as there's nothing much up there and while you can take a lot of territory, you can't get anywhere to win the war, as it's isolated by jungle/uncharted forest.
For Paraguay, the best option is to have him arrive a few years before the war and have both Lopez's (the elder one was in power til '62, and you're having Lee get started a year earlier. the younger was in France at the time of Lee's arrival, so I wonder how it would play to see him return to find Lee in command?) fall in love with him and grant him unlimited power. Aside from the question of why Lee would abandon his country in a time of need, you have the problem that the younger Lopez was in love with himself and fancied himself a top general, jealous of any other military officers (the army was basically a horde with Lopez at the top and all subordinate officers stripped of any real power). Given a couple years in this hand wavium situation, though, a capable general with Lopez' backing could do wonders. Lopez spent mostly on his own palace/self and on the military, so Lee would get a lot of the supplies he wanted (getting everything is unrealistic given the short time frame and the limited ability of the country to spend). With such a scenario and Lee leading the charge, I'd say it's easily plausible to have him take Corrientes, Entre Rios, Uruguay, Buenos Aires and Rio Grande do Sul. the only real military power in the region of the triple alliance is Argentina, and a quality army can neutralize them before Brazil can get it's act together. IF Brazil decides it is in it for the long haul, Lee has the problem that it's navy (assuming it isn't decimated as OTL) can't hold off the superior Brazilian navy forever. It would be stretching it to have Lee lead a troop northward from Rio Grande do Sul through undeveloped forest to get to populated Brazil. He's conquered a lot of country that he needs to guard and Paraguay doesn't have the base to support such grande military actions. Of course, perhaps a sane commander recognizes that you don't take on both Brazil and Argentina at the same time, so he would go for one first, then the other. It has to be Argentina first, as Paraguay can't get to populated Brazil without going through Argentina, and that leads you right back to OTL. Brazil is still a tough nut to crack, especially if they militarize while Lee is busy absorbing parts of Argentina.