There are several conceivable ways to map 8edo onto the onto the Lumatone keyboard. However, only one of them is a single-period mos scale and that is using 3\8 to generate father.
Diatonic with Negative Semitone
Trying to approximate the Standard Lumatone mapping for Pythagorean using this results in a negative semitone diatonic scale which is unintuitive to play.
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Compressed (2L 1s)
Since 8edo is a small edo, this can easily be compressed down to 2L 1s to extend your range without impacting playability, which gives you a more intuitive layout and more than 12 octaves of range with plenty of repeated notes that you could split into multiple zones with different instruments.
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Diminished + Father/Pater
Since 8edo is a multiple of 4, it makes sense to divide the octave in 4, as in diminished temperament, as demonstrated in Bryan Deister's microtonal improvisation in 8edo (2024). This mapping additionally supports a 3L 2s scale, as in father/pater temperament. The range is just under 8½ octaves, which slope upwards with the rows; but even with the upwards slope, the layout has enough vertically repeated notes that it could be divided into up to four complete manuals, with some extra keys to use for percussion, etc.
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