There are many conceivable ways to map 78edo onto the onto the Lumatone keyboard. However, since it has 2 mutually-exclusive rings of 39edo fifths, the Standard Lumatone mapping for Pythagorean is not one of them. The second best 5th produces three mutually-exclusive rings of 26edo 5ths, so that doesn't work either, and the third and fourth best are out of the diatonic tuning range.
Keen
On the other hand, the keen mapping can cover the whole gamut and make harmonics easy to play together, although it needs to be expanded from 2L 8s to 10L 2s to hit every note.
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Neutral thirds
The 7L 3s neutral thirds mapping also covers the whole gamut about as efficiently as possible and keeps octaves closer to horizontal.
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Unnamed rank-3 temperament mapping
Bryan Deister has demonsrated a Lumatone mapping for 78edo that lays out scales 11L 1s (7:1 step ratio) and 6L 6s (7:6 step ratio), in microtonal improvisation in 78edo (2025). The rightward generator 7\78 is slightly sharp large septendecimal semitone ~17/16; two of them make a slightly flat biyatismic whole tone ~17/15; and six of them readh a slightly flat undecimal minor fifth ~16/11. The down-right generator 6\78 is a somewhat sharp small undevicesimal semitone ~20/19; stacking these can yield both a slightly sharp undecimal major fourth ~11/8 (as 36\78, six generators) and slightly flat undecimal minor fifth ~16/11 (as 42\78, seven down-right generators, same as six rightward generators). The range is somewhat under three octaves, with all notes represented; octaves alternate between far and near, with an overall upwards slant.
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