The Reconstruction-era US is in no state to be mounting 1910 style (or even 1840 style) southern interventions. More likely that Lerdo succeeds Juarez but faces low-level civil insurgency as the anti-Maximilian alliance built by Juarez steadily falls apart as per OTL. Power may then be taken TTL by a general that manages to create an alliance of his own, as most of the generals-- even the anti-Lerdo ones-- were (on paper) liberals who sought an effective (but autonomous from civilian meddling) army with a stable (if weak) government. They didn't want Lerdo as their commander in chief, but that doesn't mean they wanted no one as commander.
TTl's "generalissimo" might be Bernardo Reyes, who served his patron Diaz faithfully OTL but still sought power in his own right over the army and provinces. Such ambition may serve him well TTL.
The real question, though, is what happens in the Yucatan. If Reyes's relations with the "cientificos" are as poor as OTL, modernization of the army may be stalled. A less modern army will be less capable of turning the Caste War around and destroying the Maya statelet. Alternately, if TTL's generalissimo isn't as cooperative with the Great Powers as Diaz, those powers (especially Britain) may simply decide that they'd rather see the statelet continue existing even if they dont officially recognize it. The resulting political ambiguity might cause some great power tensions as a Monroe-Doctrine-waving US accuses Britain of carving up Mexico by backing Native rebels. A US of the 1880s and 1890s facing down the Ghost Dance and other Native movements in the West, may be even more paranoid about this.