Nothing too serious, but while bored I decided to replay a mission on fable to get the stranglet for the quest. At the very end of the mission, both Lodi and Ikora spawned as usual, but rather than looking like Lodi from the campaign, it was the Lodi from after the campaign dresses in his full 9 outfit with the one glowing eye.
Can't think of the mission name, but it was the one where you kill the vex gate lord.
While its probably a bug, it did make me wonder if it was intentional given time works differently on Kepler. It would be interesting if the higher difficulties were alternate timelines, which is why you have to recollect the stranglets.
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From a gameplay perspective, no. Fable and Mythic are for replayability of Campaign missions and the location on higher levels of difficulty, which leads to higher-tier loot drops (and certain Exotic Catalyst encounters only available on Mythic). As for Lodi's character model, I think it's just a case of the update to it post-campaign being permanent. It is not the case from a story perspective, either. That'd be like saying that higher difficulties in any video games are all "alternate timelines" to each other. At most, it can be argued that Mythic is the "canonical" version of events. The Guardian not only gets Strangelets from the four Story Missions, but also finds an additional four in other locations across Kepler to stabilize the singularity.